Skip to main content
SpringerLink
Log in

Fractals and Hyperspaces

  • Conference proceedings
  • © 1991

Overview

Authors:
  1. Keith R. Wicks
    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1492)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 24.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 33.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 papers)

  1. Front Matter

    Pages I-VI
    Download chapter PDF

  2. Introduction

    • Keith R. Wicks
    Pages 1-2

  3. Preliminaries

    • Keith R. Wicks
    Pages 3-12

  4. Nonstandard development of the vietoris topology

    • Keith R. Wicks
    Pages 13-28

  5. Nonstandard development of the Hausdorff metric

    • Keith R. Wicks
    Pages 29-43

  6. Hutchinson's invariant sets

    • Keith R. Wicks
    Pages 44-85

  7. Views and fractal notions

    • Keith R. Wicks
    Pages 86-130

  8. Back Matter

    Pages 131-168
    Download chapter PDF
Back to top

Keywords

About this book

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.

Bibliographic Information

  • Book Title: Fractals and Hyperspaces

  • Authors: Keith R. Wicks

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0089156

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54965-9Published: 27 November 1991

  • eBook ISBN: 978-3-540-46610-9Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 172

  • Topics: Topology, Geometry, Mathematical Logic and Foundations

Publish with us

Policies and ethics

Back to top

Search

Navigation