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Dissertations / Theses on the topic 'Compact spaces. Topological spaces. Topology'
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1
Ntantu, Ibula. "The compact-open topology on C(X)." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/76467.
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This paper investigates the compact-open topology on the set of Ck(X) of continuous real-valued functions defined on a Tychonoff space X.
More precisely, we study the following problem: If P is a topological property, does there exist a topological property Q so that Ck(X) has P if and only if X has Q?
Characterizations of many properties are obtained throughout the thesis, sometimes modulo some “mild” restrictions on the space X.
The main properties involved are summarized in a diagram in the introduction.Ph. D.
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Dolph, Bosely Laura. "Applications of elementary submodels in topology." 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:3372301.
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Bailey, Bradley S. "I-weight, special base properties and related covering properties." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Fall/Dissertation/BAILEY_BRADLEY_37.pdf.
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Price, Ray Hampton. "The property B(P,[alpha])-refinability and its relationship to generalized paracompact topological spaces." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/49871.
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The property B(P,∝)-refinability is studied and is used to obtain new covering characterizations of paracompactness, collectionwise normality, subparacompactness, d-paracompactness, a-normality, mesocompactness, and related concepts. These new characterizations both generalize and unify many well-known results.
The property B(P,∝)-refinability is strictly weaker than the property Θ-refinability. A B(P,∝)-refinement is a generalization of a σ-locally finite-closed refinement. Here ∝ is a fixed ordinal which dictates the number of "levels" in a given refinement, and P represents a property such as discreteness or local finiteness which each "level" must satisfy relative to a certain subspace.Ph. D.
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Kolat, Alycia M. "Topological Function Spaces." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1314380881.
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Al, Mahrouqi Sharifa. "Compact topological spaces inspired by combinatorial constructions." Thesis, University of East Anglia, 2013. https://ueaeprints.uea.ac.uk/43361/.
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Due to Mrówka [24], polyadic spaces are compact Hausdorff spaces that are continuous images of some power of the one point compactification αλ of a discrete space λ. It turns out that many results about polyadic spaces hold for a more general class spaces, as we shall show in this thesis. For a sequence ‾λ = {λᵢ:iΕI} of cardinals, a compact Hausdorff space X is λ‾-multiadic if it is a continuous image of Πᵢ_ΕIαλᵢ. It is easy to observe that a λ‾-multiadic space is λ-polyadic, but whether the converse is true is a motivation of this dissertation. Although the individual polyadic and multiadic spaces differ, we show that the class of polyadic spaces is the same as multiadic class! Moreover, this dissertation is concerned with the combinatorics of multiadic class that can be used to give some of their topological structure. We give a Ramsey-like property for the class of multiadic compacta called Qλ where λ is a regular cardinal. For Boolean spaces this property is equivalent to the following: every uncountable collection of clopen sets contains an uncountable subcollection which is either linked or disjoint. We give generalizations of the Standard Sierpiński graph and use them to show that the property of being κ-multiadic is not inherited by regular closed sets for arbitrarily large κ.
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Pinchuck, Andrew. "Extension theorems on L-topological spaces and L-fuzzy vector spaces." Thesis, Rhodes University, 2002. http://hdl.handle.net/10962/d1005219.
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A non-trivial example of an L-topological space, the fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.
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Miller, David. "Homotopy theory for stratified spaces." Thesis, University of Aberdeen, 2010. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=158352.
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There are many different notions of stratified spaces. This thesis concerns homotopically stratified spaces. These were defined by Frank Quinn in his paper Homotopically Stratified Sets ([16]). His definition of stratified space is very general and relates strata by “homotopy rather than geometric conditions”. This makes homotopically stratified spaces the ideal class of stratified spaces on which to define and study stratified homotopy theory. In the study of stratified spaces it is useful to examine spaces of popaths (paths which travel from lower strata to higher strata) and holinks (those spaces of popaths which immediately leave a lower stratum for their final stratum destination). It is not immediately clear that for adjacent strata these two path spaces are homotopically equivalent and even less clear that this equivalence can be constructed in a useful way. The first aim of this thesis is to prove such an equivalence exists for homotopically stratified spaces. We will define stratified analogues of the usual definitions of maps, homotopies and homotopy equivalences. Then we will provide an elementary criterion for deciding when a strongly stratified map is a stratified homotopy equivalence. This criterion states that a strongly stratified map is a stratified homotopy equivalence if and only if the induced maps on strata and holink spaces are homotopy equivalences. Using this criterion we will prove that any homotopically stratified space is stratified homotopy equivalent to a homotopically stratified space where neighborhoods of strata are mapping cylinders. Finally we will develop categorical descriptions of the class of homotopically stratified spaces up to stratified homotopy. The first of these categorical descriptions will involve categories with a topology on their object and morphism sets. The second categorical description will involve only categories with discrete object spaces.
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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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Chishwashwa, Nyumbu. "Pairings of Binary reflexive relational structures." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_7126_1256734489.
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The main purpose of this thesis is to study the interplay between relational structures and topology , and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations between the categories of topological spaces, closure spaces and relational structures. We study the 4-point non-Hausdorff model S4 weakly homotopy equivalent to the circle S1. We study pairings of some objects in the category of relational structures similar to the multiplication S4 x S4- S4 S4 fails to be order preserving for posets. Nevertheless, applying a single barycentric subdivision on S4 to get S8, an 8-point model of the circle enables us to define an order preserving poset map S8 x S8- S4. Restricted to the axes, this map yields weak homotopy equivalences S8 x S8, we obtain a version of the Hopf map S8 x S8s - SS4. This model of the Hopf map is in fact a map of non-Hausdorff double map cylinders.
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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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Gavira, Romero Alberto. "Cellular approximations of infinite loop spaces and classifying spaces." Doctoral thesis, Universitat Autònoma de Barcelona, 2014. http://hdl.handle.net/10803/133278.
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Dado un espacio topológico punteado A, E. Dror-Farjoun introduce en 1995 la noción de A-homotopía, donde A y sus suspensiones juegan el mismo papel que las esferas en homotopía clásica. Por tanto se definen los grupos de A-homotopía de un espacio punteado X como las clases de homotopía de aplicaciones definidas desde las suspensiones de A a X. La idea de CW-complejo es sustituida por la de espacio A-celular, i.e., un espacio construido mediante ciertos colímites homotópicos punteados de A de manera iterada. El concepto de aproximación celular es remplazada por la de aproximación A-celular, esto es, un espacio A-celular CWAX junto con una aplicación natural CWAX → X que induce una equivalencia entre los espacios de aplicaciones punteadas map*(A, CWAX) y map*(A, X), y por tanto un isomorfismo en grupos de A-homotopía.
Sea p un número primo. En este trabajo estudiamos la A-celularización, donde A es un espacio clasificador del tipo BZ/pm, BZ/p∞ o un producto de estos, de dos familias de espacios: los espacios ΣBZ/p-acíclios salvo p-completación, y los espacios clasificadores de grupos p-locales compactos.
En el primer caso vemos que la A-celularización de un espacio ΣBZ/p-acíclio salvo p-completación 1-conexo X es equivalente a la fibra homotópica de la racionalización X^p → (X^p)Q. Como ejemplos tenemos los espacios de lazos infinitos y las torres de Postnikov 1-conexos con segundo grupo de homotopía de torsión.
En el segundo caso, dado un grupo p-local compacto (S, F , L ), para el estudio de la celularización de |L |^p definimos el núcleo de una aplicación f : |L |^p → Y^p como el subgrupo de S formado por los elementos x tales que la restricción de f al espacio clasificador del grupo generado por x es homotópicamente trivial. Demostramos que, bajo ciertas hipótesis sobre |L |^p, si el núcleo de cierta aplicación determinante en el cálculo de la celularización es todo el p-grupo S, entonces la A-celularización de |L |^p es equivalente a la fibra homotópica de la racionalización |L |^p → (|L |^p)Q . En el caso finito somos un más precisos, demostrando que si (S, F , L ) es un grupo p-local finito entonces |L |^p es BZ/pm -celular si y solamente si dicho núcleo es igual al mínimo subgrupo de S fuertemente cerrado que contiene toda la pi-torsión para i ≤ m. En el caso de un grupo de Lie compacto y conexo probamos que existe un entero no negativo m0 tal que para todo m ≥ m0 la (BZ/p∞ x BZ/pm)-celularización de BG^p es equivalente a la fibra homotópica de la racionalización BG^p → (BG^p)Q.Given a pointed topological space A, in 1995 E. Dror-Farjoun introduced the notion of A-homotopy, where A and its suspensions play the same role of the spheres in classical homotopy. Therefore the A-homotopy groups of a pointed space X are defined as the homotopy classes of maps from the suspensions of A to X. The idea of CW-complex is replaced by the one of A-cellular space, i.e., a space constructed by certain iterated homotopy colimits from A. The concept of cellular approximation is replaced by the A-cellular approximation, this is, a space A-cellular CWAX together with a natural map CWAX → X which induces an equivalence in the mapping spaces map*(A, CWAX) and map*(A, X), and hence an isomorphism in A-homotopy groups. Let p be a prime. In this work we study the A-cellularization, where A is a classifying space of type BZ/pm, BZ/p∞, or a product of these, of two families of spaces: the ΣBZ/p-acyclic spaces up to p-completion and the classifying spaces of p-local compact groups. In the first case we prove that the A-cellularization of a 1-connected ΣBZ/p-acyclic space up to p-completion X is equivalent to the homotopy fibre of the rationalization X^p → (X^p)Q.. Examples include the 1-connected infinite loop spaces and Postnikov pieces whose second homotopy group is a torsion group. In the second case, given a p-local group compact (S, F , L ), for the study of the A-cellularization of |L |^p, we define the kernel of a map f : |L |^p → Y^ as the subgroup of S formed by the elements x which the restriction of f to the classifying space of the group generated by x is null-homotopic. Under certain assumptions on |L |^p, we show that if the kernel of a certain map, which is determinant in the computation of the A-cellularization, is the p-group S, then the A-cellularization of |L |^p is the homotopy fibre of the rationalization |L |^p → (|L |^p)Q. In the finite case we are more precise, we prove that if (S, F , L ) is a finite p- local group, then |L |^p is BZ/pm-cellular if and only if the kernel of this map is equal to the minimal strongly F -closed subgroup in S that contains all the pi-torsion for i ≤ m. In the case of a compact Lie group, we prove that there is a non-negative integer m0 such that for all m ≥ m0, the (BZ/p∞ x BZ/pm)-cellularization of BG^p is equivalent to the homotopy fibre of the rationalization BG^p → (BG^p)Q.
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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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Richter, Christian. "Entropy and the approximation of functions on compact metric and topological spaces." [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=963690264.
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Jaeger, Mitchell Smith Michel. "A study of regularity and normality." Auburn, Ala, 2009. http://hdl.handle.net/10415/1638.
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Jiang, Jixiang. "Specifying and Detecting Topological Changes to an Areal Object." Fogler Library, University of Maine, 2009. http://www.library.umaine.edu/theses/pdf/JiangJ2009.pdf.
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Tárrega, Ruiz Luis. "Interpolation and equicontinuity sets in topological groups and spaces of continuous functions." Doctoral thesis, Universitat Jaume I, 2017. http://hdl.handle.net/10803/460830.
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This thesis studies the relation between the existence of a particular sort of subsets of metric valued continuous functions on a topological space
X and the properties of the topological space itself. The dissertation relies on how the existence of subsets of continuous functions that possess
one of these two antagonist properties, almost equicontinuity and being a B-family, affects the topological space. The former property appears in
the setting of dynamical systems, and the latter is a property stronger that the concept of non-equicontinuity and it is motivated by a result of
Bourgain.
The thesis deals with the study of the existence and the properties of interpolation sets in different settings: (i) spaces of continuous functions,
(ii) topological groups and (iii) the dual of a topological group.En esta tesis se estudia la relación que hay entre la existencia de ciertos tipos de subconjuntos de funciones valuadas en un espacio métrico y definidas en un espacio topológico X y las propiedades que posee el espacio topológico X en si. La disertación se apoya en cómo la existencia de subconjuntos de funciones continuas que poseen una de estas dos propiedades antagonistas, casi equicontinuidad y ser una B-familia, afecta al espacio topológico. La primera propiedad aparece en el contexto de los sistemas dinámicos, mientras que la segunda propiedad es un concepto más fuerte que la no equicontinuidad y viene motivada por un resultado de Bourgain. A lo largo de la tesis se lidia con el estudio de la existencia y propiedades de los conjuntos de interpolación en diferentes contextos: (i) espacios de funciones continuas, (ii) grupos topológicos y (iii) el dual de un grupo topológico.
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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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Gandhi, Sohang. "Topological Generalizations of the Heisenberg Uncertainty Relation." Honors in the Major Thesis, University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/1222.
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This item is only available in print in the UCF Libraries. If this is your Honors Thesis, you can help us make it available online for use by researchers around the world by following the instructions on the distribution consent form at http://library.ucf.edu/Systems/DigitalInitiatives/DigitalCollections/InternetDistributionConsentAgreementForm.pdf You may also contact the project coordinator, Kerri Bottorff, at kerri.bottorff@ucf.edu for more information.Bachelors
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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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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 spinc-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 (spinc) Dirac operators with non-trivial kernel. Our main goal is to study the relationship between these spinc-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 spinc-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 spinc-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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Chis, Cristina. "Bounded sets in topological groups." Doctoral thesis, Universitat Jaume I, 2010. http://hdl.handle.net/10803/10502.
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A boundedness structure (bornology) on a topological space is an ideal of subsets containing all singletons, that is, closed under taking subsets and unions of finitely many elements. In this paper we deal with the structure of the whole family of bounded subsets rather than the specific properties of them by means of certain functions that we define on a metrizable topological group. Our motivation is twofold: on the one hand, we obtain useful information about the structural features of certain remarkable classes of bounded systems, cofinality, local properties, etc. For example, we estimate the cofinality of these boundedness notions. In the second part of the paper, we apply duality methods in order to obtain estimations of the size of a local base for an important class of groups. This translation, which has been widely exhibited in the Pontryagin-van Kampen duality theory of locally compact abelian groups, is often very relevant and has been extended by many authors to more general classes of topological groups. In this work we follow basically the pattern and terminology given by Vilenkin in 1998.
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Lara, Dione Andrade. "Jogos topológicos e metrizabilidade." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06012017-085337/.
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Neste trabalho apresentaremos o princípio seletivo S1(O;H ) que caracteriza a propriedade da diagonal Gd . Iremos também apresentar um jogo topológico G1(O;H ) induzido por esse princípio seletivo e estudaremos as relações entre esse jogo e a propriedade da diagonal Gd . Além disso, apresentaremos outros jogos topológicos e mostraremos quais são as relações destes com o jogo G1(O;H ). Finalmente, daremos algumas aplicações desses jogos e exemplosIn this work we present a selection principle S1(O;H) that characterizes the Gd -diagonal property. We also present a topological game G1(O;H ) induced by this selection principle and we study the relations between this game and the Gd -diagonal property. Besides that, we present other topological games and we show which are the relations between those topological games and the game G1(O;H ). Finally, we give some applications and examples.
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Moreira, Charles dos Anjos [UNESP]. "Linguagem de categorias e o Teorema de van Kampen." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/152195.
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Esse trabalho trata de elementos da Topologia Algébrica, a qual tem como fundamental aplicação abordar questões acerca de Espaços Topológicos sob o ponto de vista algébrico. Uma das questões é tentar responder se dois espaços topológicos X e Y são homeomorfos. Neste sentido, o grupo fundamental é uma ferramenta algébrica útil por se tratar de um invariante topológico. Além disso, apresentamos o Teorema de van Kampen do ponto de vista da Linguagem de Categorias e Funtores.
This work treats of elements of the Algebraic Topology, which has as fundamental application to approach subjects concerning Topological Spaces under the algebraic point of view. One of the subjects is to try to answer if two topological spaces X and Y are homeomorphics. In this sense, the fundamental group is an useful algebraic tool for treating of an topological invariant. In addition, we presented the van Kampen's Theorem of the point of view of the language of Categories and Functors.
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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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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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Larsson, David. "Algorithmic Construction of Fundamental Polygons for Certain Fuchsian Groups." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-119916.
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The work of mathematical giants, such as Lobachevsky, Gauss, Riemann, Klein and Poincaré, to name a few, lies at the foundation of the study of the highly structured Riemann surfaces, which allow definition of holomorphic maps, corresponding to analytic maps in the theory of complex analysis. A topological result of Poincaré states that every path-connected Riemann surface can be realised by a construction of identifying congruent points in the complex plane, the Riemann sphere or the hyperbolic plane; just three simply connected surfaces that cover the underlying Riemann surface. This requires the discontinuous action of a discrete subgroup of the automorphisms of the corresponding space. In the hyperbolic plane, which is the richest source for Riemann surfaces, these groups are called Fuchsian, and there are several ways to study the action of such groups geometrically by computing fundamental domains. What is accomplished in this thesis is a combination of the methods found by Reidemeister & Schreier, Singerman and Voight, and thus provides a unified way of finding Dirichlet domains for subgroups of cofinite groups with a given index. Several examples are considered in-depth.
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Pereira, Rosane Gomes. "Desigualdades universais para autovalores do polidrifting laplaciano em dominios compactos do R^n e S^n." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/5542.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work, we study eigenvalues of poly-drifting laplacian on compact Riemannian manifolds with boundary (possibly empty). Here, we bring a universal inequality for the eigenvalues of the poly-drifting operator on compact domains in an Euclidean spaceRn. Besides,weintroduce universal inequalities for eigenvalues of poly-drifting operator on compact domains in a unit n-sphere Sn. We give an universal inequality for lower order eigenvalues of the poly-drifting operator inRn and Sn. Moreover, we prove an universal inequality type Ashbaugh and Benguria for the drifting Laplacian on Riemannian manifold immersed in an unit sphere or a projective space. Let be a bounded domain in a n-dimensional Euclidean space Rn. We study eigenvalues of an eigenvalue problem of a system of elliptic equations of the drifting laplacian 8>><>>: L u+ (r(divu)r divu) = ¯ u; in ; uj@ = 0 Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, a universal inequality for lower order eigenvalues of the problem is also derived.
Neste trabalho, estudamos autovalores do polidrifting Laplaciano em variedades Riemannianas compactas com fronteira (possivelmente vazia). Aqui, trazemos uma desigualdade universal para autovalores do polidrifting operador em domínios compactos no espaço Euclidiano Rn. Além disso, introduzimos desigualdades universais para autovalores do polidrifting operador em domínios compactos na n-esfera unitária Sn. Fornecemos uma estimativa para autovalores de ordem inferior do polidrifting operador emRn e Sn. Mais ainda, provamos uma desigualdade universal do tipo Ashbaugh-Benguria para o drifting Laplacianoem variedades Riemannianas imersas em uma esfera unitária ou no espaço projetivo. Seja um domínio limitado no n-dimensional espaço Euclidiano Rn. Estudamos autovalores de um problema de autovalores de um sistema de equações elípticas do drifting Laplaciano 8>><>>: L u+ (r(divu)r divu) = ¯ u; in ; uj@ = 0 Estimativas para autovalores do problema de autovalores acima são obtidas. Além disso, uma desigualdade universal de ordem inferior também é encontrada.
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Pinchuck, Andrew. "Extension theoroms on L-topological spaces and L-fuzzy vector spaces /." 2001. http://eprints.ru.ac.za/1301/.
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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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(11205846), Pablo J. Andujar Guerrero. "DEFINABLE TOPOLOGICAL SPACES IN O-MINIMAL STRUCTURES." Thesis, 2021.
Find full textAbstract:
We further the research in o-minimal topology by studying in full generality definable topological spaces in o-minimal structures. These are topological spaces $(X, \tau)$, where $X$ is a definable set in an o-minimal structure and the topology $\tau$ has a basis that is (uniformly) definable. Examples include the canonical o-minimal "euclidean" topology, “definable spaces” in the sense of van den Dries [17], definable metric spaces [49], as well as generalizations of classical non-metrizable topological spaces such as the Split Interval and the Alexandrov Double Circle.
We develop a usable topological framework in our setting by introducing definable analogues of classical topological properties such as separability, compactness and metrizability. We characterize these notions, showing in particular that, whenever the underlying o-minimal structure expands $(\mathbb{R},<)$, definable separability and compactness are equivalent to their classical counterparts, and a similar weaker result for definable metrizability. We prove the equivalence of definable compactness and various other properties in terms of definable curves and types. We show that definable topological spaces in o-minimal expansions of ordered groups and fields have properties akin to first countability. Along the way we study o-minimal definable directed sets and types. We prove a density result for o-minimal types, and provide an elementary proof within o-minimality of a statement related to the known connection between dividing and definable types in o-minimal theories.
We prove classification and universality results for one-dimensional definable topological spaces, showing that these can be largely described in terms of a few canonical examples. We derive in particular that the three element basis conjecture of Gruenhage [25] holds for all infinite Hausdorff definable topological spaces in o-minimal structures expanding $(\mathbb{R},<)$, i.e. any such space has a definable copy of an interval with the euclidean, discrete or lower limit topology.
A definable topological space is affine if it is definably homeomorphic to a euclidean space. We prove affineness results in o-minimal expansions of ordered fields. This includes a result for Hausdorff one-dimensional definable topological spaces. We give two new proofs of an affineness theorem of Walsberg [49] for definable metric spaces. We also prove an affineness result for definable topological spaces of any dimension that are Tychonoff in a definable
sense, and derive that a large class of locally affine definable topological spaces are affine.
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"The Induced topology of local minima with applications to artificial neural networks." Chinese University of Hong Kong, 1992. http://library.cuhk.edu.hk/record=b5887050.
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by Yun Chung Chu.Thesis (M.Phil.)--Chinese University of Hong Kong, 1992.
Includes bibliographical references (leaves 163-[165]).
Chapter 1 --- Background --- p.1
Chapter 1.1 --- Introduction --- p.1
Chapter 1.2 --- Basic notations --- p.4
Chapter 1.3 --- Object of study --- p.6
Chapter 2 --- Review of Kohonen's algorithm --- p.22
Chapter 2.1 --- General form of Kohonen's algorithm --- p.22
Chapter 2.2 --- r-neighborhood by matrix --- p.25
Chapter 2.3 --- Examples --- p.28
Chapter 3 --- Local minima --- p.34
Chapter 3.1 --- Theory of local minima --- p.35
Chapter 3.2 --- Minimizing the number of local minima --- p.40
Chapter 3.3 --- Detecting the success or failure of Kohonen's algorithm --- p.48
Chapter 3.4 --- Local minima for different graph structures --- p.59
Chapter 3.5 --- Formulation by geodesic distance --- p.65
Chapter 3.6 --- Local minima and Voronoi regions --- p.67
Chapter 4 --- Induced graph --- p.70
Chapter 4.1 --- Formalism --- p.71
Chapter 4.2 --- Practical way to find the induced graph --- p.88
Chapter 4.3 --- Some examples --- p.95
Chapter 5 --- Given mapping vs induced mapping --- p.102
Chapter 5.1 --- Comparison between given mapping and induced mapping --- p.102
Chapter 5.2 --- Matching the induced mapping to given mapping --- p.115
Chapter 6 --- A special topic: application to determination of dimension --- p.131
Chapter 6.1 --- Theory --- p.133
Chapter 6.2 --- Advanced examples --- p.151
Chapter 6.3 --- Special applications --- p.156
Chapter 7 --- Conclusion --- p.159
Bibliography --- p.163
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Richter, Christian [Verfasser]. "Entropy and the approximation of functions on compact metric and topological spaces / con Christian Richter." 2001. http://d-nb.info/963690264/34.
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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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Aphane, Maggie. "On some results of analysis in metric spaces and fuzzy metric spaces." Diss., 2009. http://hdl.handle.net/10500/3224.
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The notion of a fuzzy metric space due to George and Veeramani has many
advantages in analysis since many notions and results from classical metric space
theory can be extended and generalized to the setting of fuzzy metric spaces, for
instance: the notion of completeness, completion of spaces as well as extension of
maps. The layout of the dissertation is as follows:
Chapter 1 provide the necessary background in the context of metric spaces, while
chapter 2 presents some concepts and results from classical metric spaces in the
setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy
metric spaces, among others we show that: the product of two complete fuzzy metric
spaces is also a complete fuzzy metric space.
Our main contribution is in chapter 4. We introduce the concept of a standard
fuzzy pseudo metric space and present some results on fuzzy metric identification.
Furthermore, we discuss some properties of t-nonexpansive maps.Mathematical Sciences
M. Sc. (Mathematics)
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Νιάχος, Διονύσιος. "Χώροι συναρτήσεων." Thesis, 2015. http://hdl.handle.net/10889/8632.
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Έστω C(Y,Z) το σύνολο των συνεχών συναρτήσεων από έναν τοπολογικό χώρο Υ σ' έναν τοπολογικό χώρο Ζ. Στη διπλωματική εργασία δίνουμε και μελετάμε τοπολογίες στο C(Y,Z).Let C(Y,Z) be the set of all continuous maps from a topological space Y to a topological space Z . We give and study topologies on the set C(Y,Z) .
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Πετρόπουλος, Βασίλειος. "Συμπαγείς τοπολογικοί χώροι και συμπαγοποιήσεις." Thesis, 2011. http://nemertes.lis.upatras.gr/jspui/handle/10889/4751.
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Στα δύο πρώτα κεφάλαια γίνεται μια ιστορική αναδρομή και αναφέρονται όλες οι απαραίτητες εισαγωγικές έννοιες που χρειάζονται έτσι, ώστε να γίνει απρόσκοπτα και χωρίς ασάφειες το κυρίως μέρος της εργασίας.
Στο κεφάλαιο τρία περιγράφονται και αναλύονται οι συμπαγείς τοπολογικοί χώροι. Κατά σειρά εξετάζονται οι συμπαγείς χώροι, οι συνεχείς απεικονίσεις πάνω σε συμπαγείς χώρους και τέλος οι τοπικά συμπαγείς χώροι. Επίσης περιγράφονται έννοιες συναφείς με τη συμπάγεια.
Στο τέταρτο και τελευταίο κεφάλαιο ορίζεται η έννοια της συμπαγοποίησης ενός τοπολογικού χώρου και μελετώνται κατά σειρά η συμπαγοποίηση ενός σημείου, η συμπαγοποίηση Stone – Čech και η Wallman-type συμπαγοποίηση.We study compact topological spaces. We also describe the compactification of a topological space. Especially we describe the Alexandroff, Stone-Cech and Wallman type compactifications.