X sei ein beliebiger topologiseher tlaum, ~ sei ein additives System yon Teilmengen von X. (MICHAEL betrachtet als ~ das System aller abgeschlossenen, FLAC~SMWrE~ das aller kompakten Teilmengen von X.) Wir notieren zunachst: 1. Interessant ist insbesondere der Fall des T2Axioms hier erhalten wir ein Kriterium, das Ergebnisse yon MICHAEL und FLACHS~IEYEI~ verallgemeinert. (~0(X), ~ V T~)) das l%ech6tsche oder das Hausdorifsche Trennungsaxiom erfiillt. Ziel der vorliegenden kurzen Arbeit ist die Untersuchung der Frage, warm der Raum (~(X), ~ V ~z) (bzw. Mit ~ V Tz meinen wir das Supremum der beiden Topologien im Verband aller Topologien fiir ~ (X). bei MICHAEL und wird dort als ,lower semi- finite topology" bezeichnet. fiir ~o(X)), die dutch die Subbasis erzeugt wird. Nº de ref.]~z bezeichne die Topologie ffir ~(X) (bzw. 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. 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. 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.
"Sobre este título" puede pertenecer a otra edición de este libro.ĭescripción Taschenbuch. 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.
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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