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A Cp-Theory Problem Book

Functional Equivalencies

  • Textbook
  • © 2016

Overview

Authors:
  1. Vladimir V. Tkachuk

    1. Departamento de Matematicas, Univ Autonoma Metropolitana-Iztapal, Mexico, Mexico

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  • Contains a wide variety of top-notch methods and results of Cp-theory and general topology presented with detailed proofs
  • Presents and classifies 100 open problems in Cp-theory explaining their relationship with previous research
  • Introduces the reader to the theories of u-equivalent spaces and l-equivalent spaces

Part of the book series: Problem Books in Mathematics (PBM)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Properties Preserved by Homeomorphisms of Function Spaces

    • Vladimir V. Tkachuk
    Pages 1-62

  3. Solutions of problems 001–500

    • Vladimir V. Tkachuk
    Pages 63-635

  4. Bonus results: Some Hidden Statements

    • Vladimir V. Tkachuk
    Pages 637-647

  5. Open problems

    • Vladimir V. Tkachuk
    Pages 649-664

  6. Back Matter

    Pages 665-727
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Keywords

About this book

This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces.  An exhaustive theory of t-equivalent, u-equivalent and l-equivalent spaces is developed from scratch.   The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as  the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of l-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular,  Gul'ko and Khmyleva's example of  non-preservation of  compactness by t-equivalence, Okunev's method of constructing  l-equivalent spaces and the theorem of Marciszewski and Pelant on u-invariance of absolute Borel sets.

Reviews

“The book presents a systematic exposition of functional equivalences of Tychonoff spaces and provides many major results and methods in the area of C p -theory … . intended for graduate and postgraduate students and for all those who are interested in learning more advanced results and investigation in this dynamic area of topology … . a valuable reference source for several areas of general topology that can help to inform and direct future independent research.” (Ljubiša D. Kočinac, zbMATH 1354.54001, 2017)

Authors and Affiliations

  • Departamento de Matematicas, Univ Autonoma Metropolitana-Iztapal, Mexico, Mexico

    Vladimir V. Tkachuk

About the author

Vladimir V. Tkachuk is a professor in the Department of Mathematics of the Autonomous Metropolitan University in Mexico City. He holds a PhD from Moscow State University and is the author of A Cp-Theory Problem Book: Compactness in Function Spaces (Springer, 2015), A Cp-Theory Problem Book: Special Features of Function Spaces (Springer, 2014) and A Cp-Theory Problem Book: Topological and Function Spaces (Springer, 2011). All volumes have published in the Problem Books in Mathematics series.

Bibliographic Information

  • Book Title: A Cp-Theory Problem Book

  • Book Subtitle: Functional Equivalencies

  • Authors: Vladimir V. Tkachuk

  • Series Title: Problem Books in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-24385-6

  • Publisher: Springer Cham

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

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-24383-2Published: 14 April 2016

  • Softcover ISBN: 978-3-319-79616-1Published: 19 April 2018

  • eBook ISBN: 978-3-319-24385-6Published: 05 April 2016

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: XIV, 727

  • Topics: Topology

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