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Dimension Theory

A Selection of Theorems and Counterexamples

  • Michael G. Charalambous
Book

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

Table of contents

  1. Front Matter
    Pages i-x
  2. Michael G. Charalambous
    Pages 1-6
  3. Michael G. Charalambous
    Pages 7-13
  4. Michael G. Charalambous
    Pages 15-22
  5. Michael G. Charalambous
    Pages 23-26
  6. Michael G. Charalambous
    Pages 27-30
  7. Michael G. Charalambous
    Pages 31-35
  8. Michael G. Charalambous
    Pages 61-74
  9. Michael G. Charalambous
    Pages 85-98
  10. Michael G. Charalambous
    Pages 99-105
  11. Michael G. Charalambous
    Pages 115-127
  12. Michael G. Charalambous
    Pages 129-137
  13. Michael G. Charalambous
    Pages 147-152
  14. Michael G. Charalambous
    Pages 155-164
  15. Michael G. Charalambous
    Pages 171-181
  16. Michael G. Charalambous
    Pages 183-186
  17. Michael G. Charalambous
    Pages 187-200
  18. Michael G. Charalambous
    Pages 205-212
  19. Michael G. Charalambous
    Pages 213-222
  20. Michael G. Charalambous
    Pages 223-229
  21. Michael G. Charalambous
    Pages 231-234
  22. Michael G. Charalambous
    Pages 245-250
  23. Back Matter
    Pages 251-261

About this book

Introduction

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.

Keywords

covering dimension inductive dimension metric spaces normal spaces perfectly normal spaces Tychonoff spaces Lindelof spaces N-compact spaces dimension theory

Authors and affiliations

  • Michael G. Charalambous
    • 1
  1. 1.Department of MathematicsUniversity of the AegeanKarlovassiGreece

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-22232-1
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-22231-4
  • Online ISBN 978-3-030-22232-1
  • Series Print ISSN 1875-7634
  • Series Online ISSN 2215-1885
  • Buy this book on publisher's site