Shape Theory And Hyperspaces
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Shape Theory And Hyperspaces
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Author : Aleksandar B. Vučić
language : en
Publisher:
Release Date : 1986
Shape Theory And Hyperspaces written by Aleksandar B. Vučić and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Hyperspace categories.
Hyperspaces Shape Theory And Computational Topology
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Author : Diego Mondéjar Ruiz
language : en
Publisher:
Release Date : 2015
Hyperspaces Shape Theory And Computational Topology written by Diego Mondéjar Ruiz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This thesis is about approximations of metric compacta. The approximation and reconstruction of topological spaces using simpler ones is an old theme in geometric topology. One would like to construct a very simple space as similar as possible to the original space. Since it is very difficult (or does not make sense) to obtain a homeomorphic copy, the goal will be to find an space preserving some (algebraic) topological properties such as compactness, connectedness, separation axioms, homotopy type, homotopy and homology groups, etc. The first candidates to act as the simple spaces reproducing some properties of the original space are polyhedra. See the survey [45] for the main results. In the very beginnings of this idea, we must recall the studies of Alexandroff around 1920, relating the dimension of compact metric spaces with dimension of polyhedra by means of maps with controlled (in terms of distance) images or preimages. In a more modern framework, the idea of approximation can be carried out constructing a simplicial complex, based on our space, such as the Vietoris-Rips complex or the Cech complex, and compare its realization with it. In this direction, for example, we find the classical Nerve Lemma [12, 21] which claims that for a “good enough" open cover of the space (meaning an open covering with contractible or empty members and intersections), the nerve of the cover has the homotopy type of our original space. The problem is to find those good covers (if they exist). For Riemannian manifolds, there are some results concerning its approximation by means of the Vietoris-Rips complex. Hausmann showed [35] that the realization of the Vietoris-Rips complex of the manifold, for a small enough parameter choice, has the homotopy type of the manifold. In [40], Latschev proved a conjecture made by Hausmann: The homotopy type of the manifold can be recovered using only a (dense enough) finite set of points of it, for the Vietoris-Rips complex. The results of Petersen [58], comparing the Gromov-Hausdorff distance of metric compacta with their homotopy types, are also interesting. Here, polyhedra are just used in the proofs, not in the results...
Shape Theory
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Author : S. Mardešic
language : en
Publisher: Elsevier
Release Date : 1982-01-01
Shape Theory written by S. Mardešic and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Mathematics categories.
North-Holland Mathematical Library, Volume 26: Shape Theory: The Inverse System Approach presents a systematic introduction to shape theory by providing background materials, motivation, and examples, including shape theory and invariants, pro-groups, shape fibrations, and metric compacta. The publication first ponders on the foundations of shape theory and shape invariants. Discussions focus on the stability and movability of spaces, homotopy and homology pro-groups, shape dimension, inverse limits and shape of compacta, topological shape, and absolute neighborhood retracts. The text then takes a look at a survey of selected topics, including basic topological constructions and shape, shape dimension of metric compacta, complement theorems of shape theory, shape fibrations, and cell-like maps. The text ponders on polyhedra and Borsuk's approach to shape. Topics include shape category of metric compacta and metric pairs, homotopy type of polyhedra, and topology of simplicial complexes. The publication is a valuable source of data for researchers interested in the inverse system approach.
Shape Theory
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Author : Jerzy Dydak
language : en
Publisher: Springer Verlag
Release Date : 1978
Shape Theory written by Jerzy Dydak and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Fractals And Hyperspaces
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Author : Keith R. Wicks
language : en
Publisher: Springer
Release Date : 2006-11-14
Fractals And Hyperspaces written by Keith R. Wicks and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal", i.e. have infinite detail in a certain sense. These ideas have considerable scope for further development, and a list of problems and lines of research is included.
Hyperspaces
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Author : Alejandro Illanes
language : en
Publisher: CRC Press
Release Date : 1999-01-04
Hyperspaces written by Alejandro Illanes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-04 with Mathematics categories.
Presents hyperspace fundamentals, offering a basic overview and a foundation for further study. Topics include the topology for hyperspaces, examples of geometric models for hyperspaces, 2x and C(X) for Peano continua X, arcs in hyperspaces, the shape and contractability of hyperspaces, hyperspaces and the fixed point property, and Whitney maps. The text contains examples and exercises throughout, and provides proofs for most results.
The Shape Of Inner Space
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Author : Shing-Tung Yau
language : en
Publisher: Il Saggiatore
Release Date : 2010-09-07
The Shape Of Inner Space written by Shing-Tung Yau and has been published by Il Saggiatore this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-07 with Mathematics categories.
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
Shape Theory And Topological Sciences
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Author :
language : en
Publisher:
Release Date : 1981
Shape Theory And Topological Sciences written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Shape Theory On Compact Hausdorff Spaces
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Author : Kenneth Lynn Coffman
language : en
Publisher:
Release Date : 1973
Shape Theory On Compact Hausdorff Spaces written by Kenneth Lynn Coffman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Generalized spaces categories.
Glasnik Matematicki
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Author :
language : en
Publisher:
Release Date : 1997-06
Glasnik Matematicki written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06 with categories.