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 much more slickly than before. 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.
Language eng Summary 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. Label Fractals and hyperspaces Title Fractals and hyperspaces Statement of responsibility Keith R. These ideas have considerable scope for further development, and a list of problems and lines of research is included.
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. 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. Englisch.Summary 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. 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. 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. Druck auf Anfrage Neuware -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.
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