Rozprawy doktorskie: „Mapping (Mathematics) Topological spaces”

1

Stover, Derrick D. "Continuous Mappings and Some New Classes of Spaces". View abstract, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3371579.

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Jones, Leslie Braziel Raines Brian Edward. "Adding machines". Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5311.

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Thompson, Scotty L. "Comparing Topological Spaces Using New Approaches to Cleavability". View abstract, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3372574.

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Kaczynski, Tomasz. "Topological transversality of condensing set-valued maps". Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=73995.

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Abu, Safiya Abdul Sami'e Muhammad. "Bifuzzy topological spaces". Thesis, City University London, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358109.

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6

Kolat, Alycia M. "Topological Function Spaces". Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1314380881.

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7

Moody, Philip. "Neighbourhood conditions on topological spaces". Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236175.

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8

Nada, S. I. M. "Studies on topological ordered spaces". Thesis, University of Southampton, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376798.

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Nielsen, Mark J. "Tilings of topological vector spaces /". Thesis, Connect to this title online; UW restricted, 1990. http://hdl.handle.net/1773/5763.

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Ntumba, Patrice Pungu. "DW complexes and their underlying topological spaces". Doctoral thesis, University of Cape Town, 2001. http://hdl.handle.net/11427/4915.

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Bibliography: leaves 126-128.
The naive concept of a DW complex is that of a differential space that can be built up from cells and whose differential structure is defined in terms of differential structures on euclidean unit closed balls. This concept stems from an analogue in the category of topological spaces: the so-called CW complex (introduced by J.H.C. Whitehead in 1949).

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11

Muhamed, Abera Ayalew. "Moduli spaces of topological solitons". Thesis, University of Kent, 2015. https://kar.kent.ac.uk/47961/.

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This thesis presents a detailed study of phenomena related to topological solitons (in $2$-dimensions). Topological solitons are smooth, localised, finite energy solutions in non-linear field theories. The problems are about the moduli spaces of lumps in the projective plane and vortices on compact Riemann surfaces. Harmonic maps that minimize the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions in real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences for the behaviour of lumps and their symmetries. An interesting feature is that the moduli space of charge $3$ lumps is a $7$- dimensional manifold of cohomogeneity one. In this thesis, we discuss the charge $3$ moduli space, calculate its metric and find explicit formula for various geometric quantities. We discuss the moment of inertia (or angular integral) of moduli spaces of charge $3$ lumps. We also discuss the implications for lump decay. We discuss interesting families of moduli spaces of charge $5$ lumps using the symmetry property and Riemann-Hurwitz formula. We discuss the K\"ahler potential for lumps and find an explicit formula on the $1$-dimensional charge $3$ lumps. The metric on the moduli spaces of vortices on compact Riemann surfaces where the fields have zeros of positive multiplicity is evaluated. We calculate the metric, K\"{a}hler potential and scalar curvature on the moduli spaces of hyperbolic $3$- and some submanifolds of $4$-vortices. We construct collinear hyperbolic $3$- and $4$-vortices and derive explicit formula of their corresponding metrics. We find interesting subspaces in both $3$- and $4$-vortices on the hyperbolic plane and find an explicit formula for their respective metrics and scalar curvatures. We first investigate the metric on the totally geodesic submanifold $\Sigma_{n,m},\, n+m=N$ of the moduli space $M_N$ of hyperbolic $N$-vortices. In this thesis, we discuss the K\"{a}hler potential on $\Sigma_{n,m}$ and an explicit formula shall be derived in three different approaches. The first is using the direct definition of K\"ahler potential. The second is based on the regularized action in Liouville theory. The third method is applying a scaling argument. All the three methods give the same result. We discuss the geometry of $\Sigma_{n,m}$, in particular when $n=m=2$ and $m=n-1$. We evaluate the vortex scattering angle-impact parameter relation and discuss the $\frac{\pi}{2}$ vortex scattering of the space $\Sigma_{2,2}$. Moreover, we study the $\frac{\pi}{n}$ vortex scattering of the space $\Sigma_{n,n-1}$. We also compute the scalar curvature of $\Sigma_{n,m}$. Finally, we discuss vortices with impurities and calculate explicit metrics in the presence of impurities.

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12

Mielke, Thomas Martin. "Mapping spaces, configuration spaces and gauge theory". Thesis, University of Warwick, 1995. http://wrap.warwick.ac.uk/109201/.

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The present thesis considers the space of connections modulo based gauge equivalence on a principal SU(2) bundle over a closed simply-connected smooth four-dimensional manifold M. Up to homotopy equivalence, this is the space of basepoint-preserving maps from M to BSU('2), the classifying space of SU(2). It depends only on the homotopy type of M which is characterized by the intersection form. The Z/pZ-homology of the mapping space for p a prime not equal to 3 is computed and given in terms of the data associated to the intersection form. For the prime 3, partial results are obtained. The main method is to consider a fibration associated to a CW decomposition of M and to show that the corresponding Eilenberg- Moore spectral sequence collapses. These results generalize from manifolds to spaces homotopy equivalent to a bouquet of 2-spheres with a single 4-cell attached. For the possible homotopy types the space of connections modulo gauge equivalence ran attain, a classification is obtained in the following sense. The homotopy type of this space is uniquely determined by the rank, type and signature modulo eight of the intersection form. On the other hand, the homotopy type determines the rank, type and signature modulo four of the intersection form. Both results together give a complete classification for the case of spin manifolds. The homotopy types of the spaces of connections modulo gauge equivalence over two spin manifolds agree if and only if the intersection forms are of the same rank. These results use a classification of unimodular bilinear forms over the ring Z/4Z. In a final part, a map is constructed from the labelled configuration spaces of points in the manifold to the mapping space. This map is shown to be asymptotically surjective in homology with Z/2Z-coefficients. For homology with general coefficients, classes are constructed which are not approximated by this map.

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13

Lamont, Julie. "Total negation in general topology and in ordered topological spaces". Thesis, Queen's University Belfast, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334503.

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14

Spadaro, Santi Gruenhage Gary F. "Discrete sets, free sequences and cardinal properties of topological spaces". Auburn, Ala, 2009. http://hdl.handle.net/10415/1757.

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15

Orpen, David Lisle. "Characterization of stratified L-topological spaces by convergence of stratified L-filters". Thesis, Rhodes University, 2011. http://hdl.handle.net/10962/d1005216.

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For the case where L is an ecl-premonoid, we explore various characterizations of SL-topological spaces, in particular characterization in terms of a convergence function lim: FS L(X) ! LX. We find we have to introduce a new axiom , L on the lim function in order to completely describe SL-topological spaces, which is not required in the case where L is a frame. We generalize the classical Kowalski and Fischer axioms to the lattice context and examine their relationship to the convergence axioms. We define the category of stratified L-generalized convergence spaces, as a generalization of the classical convergence spaces and investigate conditions under which it contains the category of stratified L-topological spaces as a reflective subcategory. We investigate some subcategories of the category of stratified L-generalized convergence spaces obtained by generalizing various classical convergence axioms.

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16

Razafindrakoto, Ando Desire. "Neighbourhood operators on Categories". Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/80169.

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Thesis (PhD)--Stellenbosch University, 2013.
ENGLISH ABSTRACT: While the notions of open and closed subsets in a topological space are dual to each other, they take on another meaning when points and complements are no longer available. Closure operators have been extensively used to study topological notions on categories. Though this has recovered a fair amount of topological results and has brought an economy of e ort and insight into Topology, it is thought that certain properties, such as convergence, are naturally associated with neighbourhoods. On the other hand, it is interesting enough to investigate certain notions, such as that of closed maps, which in turn are naturally associated with closure by means of neighbourhoods. We propose in this thesis a set of axioms for neighbourhoods and test them with the properties of connectedness and compactness.
AFRIKAANSE OPSOMMING: Al is die twee konsepte van oop en geslote subversamelings in 'n topologiese ruimte teenoorgesteldes van mekaar, verander hul betekenis wanneer punte en komplemente nie meer ter sprake is nie. Die gebruik van afsluitingsoperatore is alreeds omvattend in die studie van topologiese konsepte in kategorieë, toegepas. Alhoewel 'n redelike aantal topologiese resultate, groeiende belangstelling en groter insig tot Topologie die gevolg was, word daar geglo dat seker eienskappe, soos konvergensie, op 'n natuurlike wyse aan omgewings verwant is. Nietemin is dit van belang om sekere eienskappe, soos geslote afbeeldings, wat natuurlik verwant is aan afsluiting, te bestudeer. In hierdie proefskrif stel ons 'n aantal aksiomas oor omgewings voor en toets dit gevolglik met die eienskappe van samehangendheid en kompaktheid.

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17

Chowdhury, Samir. "Metric and Topological Approaches to Network Data Analysis". The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555420352147114.

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18

French, Jennifer E. "Derived mapping spaces as models for localizations by Jennifer E. French". Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/59781.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 71-73).
This work focuses on a generalization of the models for rational homotopy theory developed by D. Sullivan and D. Quillen and p-adic homotopy developed by M. Mandell to K(1)-local homotopy theory. The work is divided into two parts. The first part is a reflection on M. Mandell's model for p-adic homotopy theory. Reformulating M. Mandell's result in terms of an adjunction between p-complete, nilpotent spaces of finite type and a subcategory of commutative HIF,-algebras, the main theorem shows that the unit of this adjunction induces an isomorphism between the unstable HF, Adams spectral sequence and the HIF, Goerss-Hopkins spectral sequence. The second part generalizes M. Mandell's model for p-adic homotopy theory to give a model for K(1)-localization. The main theorem gives a model for the K(1)- localization of an infinite loop space as a certain derived mapping space of K(1)- local ring spectra. This result is proven by analyzing a more general functor from finite spectra to a mapping space of K -algebras using homotopy calculus, and then taking the continuous homotopy fixed points with respect to the prime to p Adams operations.
Ph.D.

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19

Peske, Wendy Ann. "A topological approach to nonlinear analysis". CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2779.

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A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed point theorem to Schauder's fixed point theorem, and Picard's theorem.

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20

Zhou, Jie. "Arithmetic Properties of Moduli Spaces and Topological String Partition Functions of Some Calabi-Yau Threefolds". Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11352.

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This thesis studies certain aspects of the global properties, including geometric and arithmetic, of the moduli spaces of complex structures of some special Calabi-Yau threefolds (B-model), and of the corresponding topological string partition functions defined from them which are closely related to the generating functions of Gromov-Witten invariants of their mirror Calabi-Yau threefolds (A-model) by the mirror symmetry conjecture.
Mathematics

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21

Hiers, Nathaniel Christopher. "Equivalence of the Rothberger and k-Rothberger Games for Hausdorff Spaces". Thesis, University of North Texas, 2019. https://digital.library.unt.edu/ark:/67531/metadc1505207/.

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First, we show that the Rothberger and 2-Rothberger games are equivalent. Then we adjust the former proof and introduce another game, the restricted Menger game, in order to obtain a broader result. This provides an answer in the context of Hausdorff spaces for an open question posed by Aurichi, Bella, and Dias.

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22

Karatas, Sinem Ayse. "Remainders and Connectedness of Ordered Compactifications". TopSCHOLAR®, 2012. http://digitalcommons.wku.edu/theses/1156.

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The aim of this thesis is to establish the principal properties for the theory of ordered compactifications relating to connectedness and to provide particular examples. The initial idea of this subject is based on the notion of the Stone-Cech compactification.The ordered Stone-Cech compactification oX of an ordered topological space X is constructed analogously to the Stone-Cech compactification X of a topological space X, and has similar properties. This technique requires a conceptual understanding of the Stone-Cech compactification and how its product applies to the construction of ordered topological spaces with continuous increasing functions. Chapter 1 introduces background information. Chapter 2 addresses connectedness and compactification. If (A;B) is a separation ofa topological space X, then (A 8 B) = A 8 B, but in the ordered setting, o(A 8 B)need not be oA 8 oB. We give an additional hypothesis on the separation (A;B) tomake o(A 8 B) = oA 8 oB. An open question in topology is when is X -X = X. Weanswer the analogous question for ordered compactifications of totally ordered spaces. So, we are concerned with the remainder, that is, the set of added points oX -X. Wedemonstrate the topological properties by using lters. Moreover, results of lattice theory turn out to be some of the basic tools in our original approach. In Chapter 3, specific examples and counterexamples are given to illustrate earlierresults.

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23

Leung, Wai-Man Raymond. "On spin c-invariants of four-manifolds". Thesis, University of Oxford, 1995. http://ora.ox.ac.uk/objects/uuid:a9790f36-748f-4574-a97c-4f416ca67207.

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The spin^c-invariants for a compact smooth simply-connected oriented four-manifold, as defined by Pidstrigach and Tyurin, are studied in this thesis. Unlike the Donaldson polynomial invariants, they are defined by cutting down the moduli space M' of '1-instantons', which is the subspace of the moduli space M of anti-self-dual connections parametrizing coupled (spin^c) Dirac operators with non-trivial kernel. Our main goal is to study the relationship between these spin^c-invariants and the Donaldson polynomial invariants. The 'jumping subset' M' defined a cohomology class P of M which is given by the generalised Porteous formula. When the index l of the coupled Dirac operator is 1, the two smooth invariants are the same by definition. When l = 0 (or when M is compact), the spin^c-invariants are expressable as a Donaldson polynomial evaluating the 'Porteous class' P. Our main results concern the first two non-trivial cases l = -1 and -2, when the generalised Porteous formula can not be applied directly. Using cut-and-paste arguments to the moduli space M, we show that for the former case the spin^c-invariants and the contracted Donaldson invariants differ by a correction term. It is the number of points in the immediate lower stratum of the Uhlenbeck compactification times a universal 'linking invariant' on S⁴, which is obtained by computing an example (the K3 surface). The case when l = -2 and dimM = 8 is a parametrized version of the l = -1 situation and the correction term, which involves the same 'linking invariant', is obtained from a suitable obstruction theory.

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24

Hume, David S. "Embeddings of infinite groups into Banach spaces". Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde.

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In this thesis we build on the theory concerning the metric geometry of relatively hyperbolic and mapping class groups, especially with respect to the difficulty of embedding such groups into Banach spaces. In Chapter 3 (joint with Alessandro Sisto) we construct simple embeddings of closed graph manifold groups into a product of three metric trees, answering positively a conjecture of Smirnov concerning the Assouad-Nagata dimension of such spaces. Consequently, we obtain optimal embeddings of such spaces into certain Banach spaces. The ideas here have been extended to other closed three-manifolds and to higher dimensional analogues of graph manifolds. In Chapter 4 we give an explicit method of embedding relatively hyperbolic groups into certain Banach spaces, which yields optimal bounds on the compression exponent of such groups relative to their peripheral subgroups. From this we deduce that the fundamental group of every closed three-manifold has Hilbert compression exponent one. In Chapter 5 we prove that relatively hyperbolic spaces with a tree-graded quasi-isometry representative can be characterised by a relative version of Manning's bottleneck property. This applies to the Bestvina-Bromberg-Fujiwara quasi-trees of spaces, yielding an embedding of each mapping class group of a closed surface into a finite product of simplicial trees. From this we obtain explicit embeddings of mapping class groups into certain Banach spaces and deduce that these groups have finite Assouad-Nagata dimension. It also applies to relatively hyperbolic groups, proving that such groups have finite Assouad-Nagata dimension if and only if each peripheral subgroup does.

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25

Ruth, Harry Leonard Jr. "Conformal densities and deformations of uniform loewner metric spaces". Cincinnati, Ohio : University of Cincinnati, 2008. http://www.ohiolink.edu/etd/view.cgi?ucin1210203872.

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Thesis (Ph.D.)--University of Cincinnati, 2008.
Committee/Advisors: David Herron PhD (Committee Chair), David Minda PhD (Committee Member), Nageswari Shanmugalingam PhD (Committee Member). Title from electronic thesis title page (viewed Sep.3, 2008). Keywords: conformal density; uniform spaces; Loewner; quasisymmetry; quasiconofrmal. Includes abstract. Includes bibliographical references.

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26

Rees, Michael K. "Topological uniqueness results for the special linear and other classical Lie Algebras". Thesis, University of North Texas, 2001. https://digital.library.unt.edu/ark:/67531/metadc3000/.

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Suppose L is a complete separable metric topological group (ring, field, etc.). L is topologically unique if the Polish topology on L is uniquely determined by its underlying algebraic structure. More specifically, L is topologically unique if an algebraic isomorphism of L with any other complete separable metric topological group (ring, field, etc.) induces a topological isomorphism. A local field is a locally compact topological field with non-discrete topology. The only local fields (up to isomorphism) are the real, complex, and p-adic numbers, finite extensions of the p-adic numbers, and fields of formal power series over finite fields. We establish the topological uniqueness of the special linear Lie algebras over local fields other than the complex numbers (for which this result is not true) in the context of complete separable metric Lie rings. Along the way the topological uniqueness of all local fields other than the field of complex numbers is established, which is derived as a corollary to more general principles which can be applied to a larger class of topological fields. Lastly, also in the context of complete separable metric Lie rings, the topological uniqueness of the special linear Lie algebra over the real division algebra of quaternions, the special orthogonal Lie algebras, and the special unitary Lie algebras is proved.

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27

Lesser, Alice. "Optimal and Hereditarily Optimal Realizations of Metric Spaces". Doctoral thesis, Uppsala University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8297.

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This PhD thesis, consisting of an introduction, four papers, and some supplementary results, studies the problem of finding an optimal realization of a given finite metric space: a weighted graph which preserves the metric's distances and has minimal total edge weight. This problem is known to be NP-hard, and solutions are not necessarily unique.

It has been conjectured that extremally weighted optimal realizations may be found as subgraphs of the hereditarily optimal realization Γ_d, a graph which in general has a higher total edge weight than the optimal realization but has the advantages of being unique, and possible to construct explicitly via the tight span of the metric.

In Paper I, we prove that the graph Γ_d is equivalent to the 1-skeleton of the tight span precisely when the metric considered is totally split-decomposable. For the subset of totally split-decomposable metrics known as consistent metrics this implies that Γ_d is isomorphic to the easily constructed Buneman graph.

In Paper II, we show that for any metric on at most five points, any optimal realization can be found as a subgraph of Γ_d.

In Paper III we provide a series of counterexamples; metrics for which there exist extremally weighted optimal realizations which are not subgraphs of Γ_d. However, for these examples there also exists at least one optimal realization which is a subgraph.

Finally, Paper IV examines a weakened conjecture suggested by the above counterexamples: can we always find some optimal realization as a subgraph in Γ_d? Defining extremal optimal realizations as those having the maximum possible number of shortest paths, we prove that any embedding of the vertices of an extremal optimal realization into Γ_d is injective. Moreover, we prove that this weakened conjecture holds for the subset of consistent metrics which have a 2-dimensional tight span

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28

Gonzalez, Villasanti Hugo Jose. "Stability of Input/Output Dynamical Systems on Metric Spaces: Theory and Applications". The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu155558269238935.

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Atim, Alexandru Gabriel. "Uniqueness Results for the Infinite Unitary, Orthogonal and Associated Groups". Thesis, University of North Texas, 2008. https://digital.library.unt.edu/ark:/67531/metadc6136/.

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Let H be a separable infinite dimensional complex Hilbert space, let U(H) be the Polish topological group of unitary operators on H, let G be a Polish topological group and φ:G→U(H) an algebraic isomorphism. Then φ is a topological isomorphism. The same theorem holds for the projective unitary group, for the group of *-automorphisms of L(H) and for the complex isometry group. If H is a separable real Hilbert space with dim(H)≥3, the theorem is also true for the orthogonal group O(H), for the projective orthogonal group and for the real isometry group. The theorem fails for U(H) if H is finite dimensional complex Hilbert space.

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30

Kenny, Robert. "Orbit complexity and computable Markov partitions". University of Western Australia. School of Mathematics and Statistics, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0231.

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Markov partitions provide a 'good' mechanism of symbolic dynamics for uniformly hyperbolic systems, forming the classical foundation for the thermodynamic formalism in this setting, and remaining useful in the modern theory. Usually, however, one takes Bowen's 1970's general construction for granted, or restricts to cases with simpler geometry (as on surfaces) or more algebraic structure. This thesis examines several questions on the algorithmic content of (topological) Markov partitions, starting with the pointwise, entropy-like, topological conjugacy invariant known as orbit complexity. The relation between orbit complexity de nitions of Brudno and Galatolo is examined in general compact spaces, and used in Theorem 2.0.9 to bound the decrease in some of these quantities under semiconjugacy. A corollary, and a pointwise analogue of facts about metric entropy, is that any Markov partition produces symbolic dynamics matching the original orbit complexity at each point. A Lebesgue-typical value for orbit complexity near a hyperbolic attractor is also established (with some use of Brin-Katok local entropy), and is technically distinct from typicality statements discussed by Galatolo, Bonanno and their co-authors. Both our results are proved adapting classical arguments of Bowen for entropy. Chapters 3 and onwards consider the axiomatisation and computable construction of Markov partitions. We propose a framework of 'abstract local product structures'

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31

Bellmunt, Giralt Andratx. "Construction of right inverses of the Kirwan map". Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/396125.

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The objects studied in this thesis are Hamiltonian spaces and it is assumed that the reader is familiar with them as explained in e.g. [Can, VII-IX] or [McSa1, §5]. The usual contents of ﬁrst year graduate courses in diﬀerential geometry and algebraic topology are also assumed. We did our best eﬀort to explain or to provide useful references to anything beyond that, including some of the notions that appear in this introduction.

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Silva, Camila Tolin Santos da. "Descobrindo a Topologia : um compêndio de fundamentos teóricos e atividades lúdicas para auxiliar na formalização de conceitos topológicos no ensino básico /". Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/155883.

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Submitted by CAMILA TOLIN SANTOS DA SILVA (camilatolin@yahoo.com.br) on 2018-08-30T19:02:42Z No. of bitstreams: 1 Camila Tolin - Dissertação mestrado versão final.pdf: 53772690 bytes, checksum: e820d5f4112aab671ce28d3bd47eab57 (MD5)
Rejected by Elza Mitiko Sato null (elzasato@ibilce.unesp.br), reason: Solicitamos que realize correções na submissão seguindo as orientações abaixo: Problema 01) É necessário que o arquivo contendo a sua dissertação esteja no formato PDF (Portable Document Format) e não esteja protegido . Problema 02) A ficha catalográfica deve ser corrigida pois nela consta: ”Instituto de Biociências, Letras e Ciências Exatas”, Presidente Prudente, o nome do Câmpus de Presidente Prudente é Faculdade de Ciências e Tecnologia. Problema 03) Solicito que corrija também na descrição na natureza da pesquisa na folha de rosto e aprovação: Dissertação apresentada como parte dos requisitos para obtenção do título de Mestre, junto ao programa de Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, da Faculdade de Ciências e Tecnologia da Universidade Estadual Paulista Júlio de Mesquita Filho , Câmpus de Presidente Prudente. Problema 04) O arquivo contém 12(doze) páginas em branco (pags. 04, 06, 08, 10, 12, 14, 24, 42, 52, 82, 98 e 138) as mesmas devem retiradas pois o arquivo não pode conter páginas em branco. e deve ser corrigido também na ficha catalográfica o número de folhas. Lembramos que o arquivo depositado no repositório deve ser igual ao impresso, o rigor com o padrão da Universidade se deve ao fato de que o seu trabalho passará a ser visível mundialmente. Agradecemos a compreensão. on 2018-08-31T13:19:11Z (GMT)
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A topologia é um ramo da matemática, sutilmente entrelaçado com a Geometria, de aplicação em diversas áreas do conhecimento, cuja conceituação foi apresentada de forma expressiva nas escolas durante as décadas de 60 e 70, com o movimento educacional conhecido como Matemática Moderna. Através das mudanças curriculares, muitos temas abordados no ensino fundamental e médio foram reestruturados dentro de um conjunto de parâmetros para a organização curricular da base nacional comum, os PCN's, que normatizam a base do ensino e orientam que a matemática deve ser apresentada para o desenvolvimento de habilidades inerentes à resolução de problemas, aquisição de linguagem simbólica, modelagem e interpretação de situações cotidianas, argumentação e aplicação em situações da vida real. Portanto, esse trabalho foi elaborado com o objetivo de fornecer suporte para o ensino da topologia no ensino básico, através da compilação de fatos históricos, formalização de definições básicas de caráter introdutório como continuidade, espaços métricos, espaços topológicos, entre outros, apresentação de atividades que poderão ser trabalhadas conjuntamente com o ensino da geometria, que de forma lúdica e intuitiva, ajudarão a alicerçar a base para um futuro aprofundamento desses conceitos, auxiliando no desenvolvimento do pensamento topológico.
Topology is a branch of mathematics, subtly intertwined with geometry, of application in several areas of knowledge, whose conceptualization was presented expressively in schools during the 60s and 70s, with the educational movement known as Modern Mathematics. Through the curricular changes, many topics addressed in elementary and secondary education have been restructured within a set of parameters for the curriculum organization of the common national base, the PCNs, that normalize the base of the teaching and guide that the mathematics must be presented for the development of inherent abilities to solve problems, acquisition of symbolic language, modeling and interpretation of everyday situations, argumentation and application in real life situations. Thus, this work was developed with the purpose of providing support for the teaching of topology in basic education, through the compilation of historical facts, formalization of basic de nitions of introductory character such as continuity, metric spaces, topological spaces, among others, presentation of activities which can be worked together with the teaching geometry, which in a playful and intuitive way, will help to lay the foundation for a future deepening of these concepts, aiding in the development of topological thinking.

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33

Cavalcante, Wasthenny Vasconcelos. "Espaços Vetoriais Topológicos". Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9277.

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In this work we investigate the concept of topological vector spaces and their properties. In the rst chapter we present two sections of basic results and in the other sections we present a more general study of such spaces. In the second chapter we restrict ourselves to the real scalar eld and we study, in the context of locally convex spaces, the Hahn-Banach and Banach-Alaoglu theorems. We also build the weak, weak-star, of bounded convergence and of pointwise convergence topologies. Finally we investigate the Theorem of Banach-Steinhauss, the Open Mapping Theorem and the Closed Graph Theorem.
Neste trabalho, estudamos o conceito de espa cos vetoriais topol ogicos e suas propriedades. No primeiro cap tulo, apresentamos duas se c~oes de resultados b asicos e, nas demais se c~oes, apresentamos um estudo sobre tais espa cos de forma mais ampla. No segundo cap tulo, restringimo-nos ao corpo dos reais e fazemos um estudo sobre os espa cos localmente convexos, o Teorema de Hahn-Banach, o Teorema de Banach- Alaoglu, constru mos as topologias fraca, fraca-estrela, da converg^encia limitada e da converg^encia pontual. Por ultimo, estudamos o Teorema da Limita c~ao Uniforme, o Teorema do Gr a co Fechado e o da Aplica c~ao Aberta no contexto mais geral dos espa cos de Fr echet.

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Matlabyana, Mack Zakaria. "Coz-related and other special quotients in frames". Thesis, 2012. http://hdl.handle.net/10500/6050.

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We study various quotient maps between frames which are defined by stipulating that they satisfy certain conditions on the cozero parts of their domains and codomains. By way of example, we mention that C-quotient and C -quotient maps (as defined by Ball and Walters- Wayland [7]) are typical of the types of homomorphisms we consider in the initial parts of the thesis. To be little more precise, we study uplifting quotient maps, C1- and C2-quotient maps and show that these quotient maps possess some properties akin to those of a C-quotient maps. The study also focuses on R - and G - quotient maps and show, amongst other things, that these quotient maps coincide with the well known C - quotient maps in mildly normal frames. We also study quasi-F frames and give a ring-theoretic characterization that L is quasi-F precisely when the ring RL is quasi-B´ezout. We also show that quasi-F frames are preserved and reflected by dense coz-onto R -quotient maps. We characterize normality and some of its weaker forms in terms of some of these quotient maps. Normality is characterized in terms of uplifting quotient maps, -normally separated frames in terms of C1-quotient maps and mild normality in terms of R - and G -quotient maps. Finally we define cozero complemented frames and show that they are preserved and reflected by dense z#- quotient maps. We end by giving ring-theoretic characterizations of these frames.
Mathematical Science
D. Phil. (Mathematics)

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35

Mirani, Mozhgan. "Classical trees and compact ultrametric spaces". Diss., 2006. http://etd.library.vanderbilt.edu/ETD-db/available/etd-03272006-143429/.

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36

(8844734), Ling Xu. "Harmomic maps into Teichmuller spaces and superrigidity of mapping class groups". Thesis, 2020.

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In the first part of the present work, we will study the harmonic maps onto Teichm\"uller space. We will formulate a general Bochner type formula for harmonic maps into Teichm\"uller space. We will also prove the existence theorem of equivariant harmonic maps from a symmetric space with finite volume into its Weil-Petersson completion $\overline{\mathcal{T}}$, by deforming an almost finite energy map in the sense of Saper into a finite energy map.

In the second part of the work, we discuss the superrigidity of mapping class group. We will provide a geometric proof of both the high rank and the rank one superrigidity of mapping class groups due to Farb-Masur and Yeung.

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Ibrahim, Caroline Maher Boulis Heil Wolfgang. "Finite abelian group actions on orientable circle bundles over surfaces". 2004. http://etd.lib.fsu.edu/theses/available/etd-07122004-135529.

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Thesis (Ph. D.)--Florida State University, 2004.
Advisor: Dr. Wolfgang Heil, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (viewed Sept. 28, 2004). Includes bibliographical references.

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38

"On density theorems, connectedness results and error bounds in vector optimization". 2001. http://library.cuhk.edu.hk/record=b5890681.

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Yung Hon-wai.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.
Includes bibliographical references (leaves 133-139).
Abstracts in English and Chinese.
Chapter 0 --- Introduction --- p.1
Chapter 1 --- Density Theorems in Vector Optimization --- p.7
Chapter 1.1 --- Preliminary --- p.7
Chapter 1.2 --- The Arrow-Barankin-Blackwell Theorem in Normed Spaces --- p.14
Chapter 1.3 --- The Arrow-Barankin-Blackwell Theorem in Topolog- ical Vector Spaces --- p.27
Chapter 1.4 --- Density Results in Dual Space Setting --- p.32
Chapter 2 --- Density Theorem for Super Efficiency --- p.45
Chapter 2.1 --- Definition and Criteria for Super Efficiency --- p.45
Chapter 2.2 --- Henig Proper Efficiency --- p.53
Chapter 2.3 --- Density Theorem for Super Efficiency --- p.58
Chapter 3 --- Connectedness Results in Vector Optimization --- p.63
Chapter 3.1 --- Set-valued Maps --- p.64
Chapter 3.2 --- The Contractibility of the Efficient Point Sets --- p.67
Chapter 3.3 --- Connectedness Results in Vector Optimization Prob- lems --- p.83
Chapter 4 --- Error Bounds In Normed Spaces --- p.90
Chapter 4.1 --- Error Bounds of Lower Semicontinuous Functionsin Normed Spaces --- p.91
Chapter 4.2 --- Error Bounds of Lower Semicontinuous Convex Func- tions in Reflexive Banach Spaces --- p.100
Chapter 4.3 --- Error Bounds with Fractional Exponents --- p.105
Chapter 4.4 --- An Application to Quadratic Functions --- p.114
Bibliography --- p.133

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"Surface registration using quasi-conformal Teichmüller theory and its application to texture mapping". 2013. http://library.cuhk.edu.hk/record=b5884501.

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Lam, Ka Chun.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 64-68).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts also in Chinese.

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"Exploration, Mapping and Scalar Field Estimation using a Swarm of Resource-Constrained Robots". Doctoral diss., 2018. http://hdl.handle.net/2286/R.I.51727.

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abstract: Robotic swarms can potentially perform complicated tasks such as exploration and mapping at large space and time scales in a parallel and robust fashion. This thesis presents strategies for mapping environmental features of interest – specifically obstacles, collision-free paths, generating a metric map and estimating scalar density fields– in an unknown domain using data obtained by a swarm of resource-constrained robots. First, an approach was developed for mapping a single obstacle using a swarm of point-mass robots with both directed and random motion. The swarm population dynamics are modeled by a set of advection-diffusion-reaction partial differential equations (PDEs) in which a spatially-dependent indicator function marks the presence or absence of the obstacle in the domain. The indicator function is estimated by solving an optimization problem with PDEs as constraints. Second, a methodology for constructing a topological map of an unknown environment was proposed, which indicates collision-free paths for navigation, from data collected by a swarm of finite-sized robots. As an initial step, the number of topological features in the domain was quantified by applying tools from algebraic topology, to a probability function over the explored region that indicates the presence of obstacles. A topological map of the domain is then generated using a graph-based wave propagation algorithm. This approach is further extended, enabling the technique to construct a metric map of an unknown domain with obstacles using uncertain position data collected by a swarm of resource-constrained robots, filtered using intensity measurements of an external signal. Next, a distributed method was developed to construct the occupancy grid map of an unknown environment using a swarm of inexpensive robots or mobile sensors with limited communication. In addition to this, an exploration strategy which combines information theoretic ideas with Levy walks was also proposed. Finally, the problem of reconstructing a two-dimensional scalar field using observations from a subset of a sensor network in which each node communicates its local measurements to its neighboring nodes was addressed. This problem reduces to estimating the initial condition of a large interconnected system with first-order linear dynamics, which can be solved as an optimization problem.
Dissertation/Thesis
Doctoral Dissertation Mechanical Engineering 2018

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