Hyperspaces

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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.

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.