and a great selection of related books, art and collectibles available now at. These ideas have considerable scope for further development, and a list of problems and lines of research is included. Fractals and Hyperspaces (Lecture Notes in Mathematics) by Wicks, Keith R. 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. 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.
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