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  • Textbook
  • © 1990

Measure, Topology, and Fractal Geometry

Authors:

  1. Gerald A. Edgar

    1. Department of Mathematics, The Ohio State University, Columbus, USA

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Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
    PDF

  2. Fractal Examples

    • Gerald A. Edgar
    Pages 1-36

  3. Metric Topology

    • Gerald A. Edgar
    Pages 37-78

  4. Topological Dimension

    • Gerald A. Edgar
    Pages 79-104

  5. Self-Similarity

    • Gerald A. Edgar
    Pages 105-122

  6. Measure Theory

    • Gerald A. Edgar
    Pages 123-146

  7. Hausdorff Dimension

    • Gerald A. Edgar
    Pages 147-194

  8. Additional Topics

    • Gerald A. Edgar
    Pages 195-216

  9. Back Matter

    Pages 217-231
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About this book

From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1
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Keywords

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Authors and Affiliations

  • Department of Mathematics, The Ohio State University, Columbus, USA

    Gerald A. Edgar

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Bibliographic Information

  • Book Title: Measure, Topology, and Fractal Geometry

  • Authors: Gerald A. Edgar

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-4134-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1990

  • eBook ISBN: 978-1-4757-4134-6Published: 17 April 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XIII, 231

  • Topics: Real Functions, Topology

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Buy it now

eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

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