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Dimension Theory

A Selection of Theorems and Counterexamples

  • Presupposed topological definitions and facts are carefully recalled
  • Includes numerous exercises proving presupposed facts
  • Includes numerous exercises of further interest
  • Helpful hints accompany exercises where necessary
  • Includes plenty of material that cannot be found elsewhere

Part of the book series: Atlantis Studies in Mathematics (ATLANTISSM, volume 7)

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Table of contents (32 chapters)

  1. Front Matter

    Pages i-x
  2. Topological Spaces

    • Michael G. Charalambous
    Pages 1-6
  3. The Three Main Dimension Functions

    • Michael G. Charalambous
    Pages 7-13
  4. The Countable Sum Theorem for Covering Dimension

    • Michael G. Charalambous
    Pages 15-22
  5. Urysohn Inequalities

    • Michael G. Charalambous
    Pages 23-26
  6. The Dimension of Euclidean Spaces

    • Michael G. Charalambous
    Pages 27-30
  7. Connected Components and Dimension

    • Michael G. Charalambous
    Pages 31-35
  8. Cozero Sets and Covering Dimension dim0

    • Michael G. Charalambous
    Pages 61-74
  9. The Inductive Dimension Ind 0

    • Michael G. Charalambous
    Pages 85-98
  10. Two Classical Examples

    • Michael G. Charalambous
    Pages 99-105
  11. Inverse Limits and N-Compact Spaces

    • Michael G. Charalambous
    Pages 115-127
  12. Some Standard Results Concerning Metric Spaces

    • Michael G. Charalambous
    Pages 129-137
  13. A Metrizable Space with Unequal Inductive Dimensions

    • Michael G. Charalambous
    Pages 147-152

About this book

This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions.


Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.

Reviews

“The monograph contains a great deal of useful and up-to-date material on dimension theory; the exposition is transparent and well organized which makes it possible to use this work both as a textbook of dimension theory and a base of research projects in numerous areas.” (Vladimir Tkachuk, zbMATH 1471.54001, 2021)

Authors and Affiliations

  • Department of Mathematics, University of the Aegean, Karlovassi, Greece

    Michael G. Charalambous

Bibliographic Information

  • Book Title: Dimension Theory

  • Book Subtitle: A Selection of Theorems and Counterexamples

  • Authors: Michael G. Charalambous

  • Series Title: Atlantis Studies in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-22232-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-22231-4Published: 18 October 2019

  • Softcover ISBN: 978-3-030-22234-5Published: 18 October 2020

  • eBook ISBN: 978-3-030-22232-1Published: 08 October 2019

  • Series ISSN: 1875-7634

  • Series E-ISSN: 2215-1885

  • Edition Number: 1

  • Number of Pages: X, 261

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Topology, Analysis

Buy it now

Buying options

eBook USD 44.99 USD 99.00
55% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.99 USD 129.99
54% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 59.99 USD 129.99
54% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access