This leads to concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal" - have infinite detail in a certain sense. The last 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. Fractals and Hyperspaces 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. 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. A major feature is that nonstandard analysis is used to obtain new proofs of some known results. The first part of the book develops certain hyperspace theories concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. These ideas have considerable scope for further development, and a list of problems and lines of research is included.Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an accessible way, complete with many figures. 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. author: Title: Fractals and Hyperspaces electronic resource / by Keith R. 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.
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