Fractals and Hyperspaces (Lecture Notes in Mathematics 1492)

Keith R. Wicks

ISBN 10: 354054965X / ISBN 13: 9783540549659

Published by Berlin, Heidelberg, New York: Springer-Verlag. Printed in Germany, 1991

About this Item

[MATH]. Keith R. Wicks. "Fractals and Hyperspaces (Lecture Notes in Mathematics 1492)." Berlin, Heidelberg, New York: Springer-Verlag. Printed in Germany, 1991. First edition thus. English language. Softcover with orange wrappers. Nonfiction academic mathematics text in nineteen sections with foreword, introduction, index, and black-and-white charts and illustrations. 9 1/2 x 6 1/2 inches. 10 oz. 176 pp. Crease in back wrapper. Toning. Text clean. Very Good. ISBN: 354054965x. "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.".

Seller Inventory # 07829

Bibliographic Details

• Title: Fractals and Hyperspaces (Lecture Notes in Mathematics 1492)
• Publisher: Berlin, Heidelberg, New York: Springer-Verlag. Printed in Germany
• Publication Date: 1991
• Language: English
• ISBN 10: 354054965X
• ISBN 13: 9783540549659
• Binding: Softcover
• Edition: First Edition.
• Condition: Very Good
• Weight: 10 ounces
• Seller catalogs:
  • Math

About this title

Synopsis

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.