Relevant bibliographies by topics / Tiling (Mathematics) Linear topological spaces

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  2. Dissertations / Theses
  3. Books

Academic literature on the topic 'Tiling (Mathematics) Linear topological spaces'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Tiling (Mathematics) Linear topological spaces"

1

Hunton, John, and James J. Walton. "Aperiodicity, rotational tiling spaces and topological space groups." Advances in Mathematics 388 (September 2021): 107855. http://dx.doi.org/10.1016/j.aim.2021.107855.

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Alberto De Bernardi, Carlo, and Libor Veselý. "Tilings of Normed Spaces." Canadian Journal of Mathematics 69, no. 02 (2017): 321–37. http://dx.doi.org/10.4153/cjm-2015-057-3.

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Abstract By a tiling of a topological linear space X, we mean a covering of X by at least two closed convex sets, called tiles, whose nonempty interiors are pairwise disjoint. Study of tilings of infinite dimensional spaceswas initiated in the 1980's with pioneer papers by V. Klee. We prove some general properties of tilings of locally convex spaces, and then apply these results to study the existence of tilings of normed and Banach spaces by tiles possessing certain smoothness or rotundity properties. For a Banach space X, our main results are the following. (i) X admits no tiling by Fréchet smooth bounded tiles. (ii) If X is locally uniformly rotund (LUR), it does not admit any tiling by balls. (iii) On the other hand, some spaces, г uncountable, do admit a tiling by pairwise disjoint LUR bounded tiles.
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KWAPISZ, JAROSLAW. "Rigidity and mapping class group for abstract tiling spaces." Ergodic Theory and Dynamical Systems 31, no. 6 (2011): 1745–83. http://dx.doi.org/10.1017/s0143385710000696.

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AbstractWe study abstract self-affine tiling actions, which are an intrinsically defined class of minimal expansive actions of ℝdon a compact space. They include the translation actions on the compact spaces associated to aperiodic repetitive tilings or Delone sets in ℝd. In the self-similar case, we show that the existence of a homeomorphism between tiling spaces implies conjugacy of the actions up to a linear rescaling. We also introduce the general linear group of an (abstract) tiling, prove its discreteness, and show that it is naturally isomorphic with the (pointed) mapping class group of the tiling space. To illustrate our theory, we compute the mapping class group for a five-fold symmetric Penrose tiling.
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KELLENDONK, JOHANNES. "Pattern equivariant functions, deformations and equivalence of tiling spaces." Ergodic Theory and Dynamical Systems 28, no. 4 (2008): 1153–76. http://dx.doi.org/10.1017/s014338570700065x.

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AbstractWe re-investigate the theory of deformations of tilings using P-equivariant cohomology. In particular, we relate the notion of asymptotically negligible shape functions introduced by Clark and Sadun to weakly P-equivariant forms. We then investigate more closely the relation between deformations of patterns and homeomorphism or topological conjugacy of pattern spaces.
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Pąk, Karol. "Linear Transformations of Euclidean Topological Spaces." Formalized Mathematics 19, no. 2 (2011): 103–8. http://dx.doi.org/10.2478/v10037-011-0016-3.

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Linear Transformations of Euclidean Topological Spaces We introduce linear transformations of Euclidean topological spaces given by a transformation matrix. Next, we prove selected properties and basic arithmetic operations on these linear transformations. Finally, we show that a linear transformation given by an invertible matrix is a homeomorphism.
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Grabowski, Janusz, and Wojciech Wojtyński. "Quotient groups of linear topological spaces." Colloquium Mathematicum 59, no. 1 (1990): 35–51. http://dx.doi.org/10.4064/cm-59-1-35-51.

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Khurana, Surjit Singh. "Vector Measures on Topological Spaces." gmj 14, no. 4 (2007): 687–98. http://dx.doi.org/10.1515/gmj.2007.687.

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Abstract Let 𝑋 be a completely regular Hausdorff space, 𝐸 a quasi-complete locally convex space, 𝐶(𝑋) (resp. 𝐶𝑏(𝑋)) the space of all (resp. all, bounded), scalar-valued continuous functions on 𝑋, and 𝐵(𝑋) and 𝐵0(𝑋) be the classes of Borel and Baire subsets of 𝑋. We study the spaces 𝑀𝑡(𝑋,𝐸), 𝑀 τ (𝑋,𝐸), 𝑀 σ (𝑋,𝐸) of tight, τ-smooth, σ-smooth, 𝐸-valued Borel and Baire measures on 𝑋. Using strict topologies, we prove some measure representation theorems of linear operators between 𝐶𝑏(𝑋) and 𝐸 and then prove some convergence theorems about integrable functions. Also, the Alexandrov's theorem is extended to the vector case and a representation theorem about the order-bounded, scalar-valued, linear maps from 𝐶(𝑋) is generalized to the vector-valued linear maps.
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DING, Yanheng. "Deformation in locally convex topological linear spaces." Science in China Series A 47, no. 5 (2004): 687. http://dx.doi.org/10.1360/03ys0025.

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Ding, Yanheng. "Deformation in locally convex topological linear spaces." Science in China Series A: Mathematics 47, no. 5 (2004): 687–710. http://dx.doi.org/10.1007/bf03036994.

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Marciszewski, Witold. "On topological embeddings of linear metric spaces." Mathematische Annalen 308, no. 1 (1997): 21–30. http://dx.doi.org/10.1007/s002080050061.

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Dissertations / Theses on the topic "Tiling (Mathematics) Linear topological spaces"

1

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

1

1940-, Beckenstein Edward, ed. Topological vector spaces. 2nd ed. Taylor & Francis, 2011.

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2

service), SpringerLink (Online, ed. Homogeneous Spaces and Equivariant Embeddings. Springer-Verlag Berlin Heidelberg, 2011.

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3

1942-, Graaf J. de, ed. Trajectory spaces, generalized functions, and unbounded operators. Springer-Verlag, 1985.

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4

Linear topologies on a ring: An overview. Longman Scientific & Technical, 1987.

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Linear topologies on a ring: An overview. Longman Scientific & Technical, 1987.

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6

Frames and bases: An introductory course. Birkhäuser, 2008.

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An introduction to frames and Riesz bases. Birkhuser, 2003.

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1929-, Hoffmann-Jørgensen J., Marcus Michael B, and Wellner Jon A. 1945-, eds. High dimensional probability III. Birkhäuser, 2003.

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Diophantine equations and power integral bases: New computational methods. Birkhäuser, 2002.

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Mineev, Vladimir P. Topologically stable defects and solitons in ordered media. Harwood Academic Publishers, 1998.

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