© 2014

A Cp-Theory Problem Book

Special Features of Function Spaces

  • Contains a wide variety of top-notch methods and results of Cp-theory and general topology presented with detailed proofs

  • Provides introductions to both descriptive and advanced set theory

  • Presents and classifies 100 open problems in Cp-theory and explains their relationship to earlier research


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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Vladimir V. Tkachuk
    Pages 45-526
  3. Vladimir V. Tkachuk
    Pages 527-537
  4. Vladimir V. Tkachuk
    Pages 539-555
  5. Back Matter
    Pages 557-583

About this book


The books in Vladimir Tkachuk’s A Cp-Theory Problem Book series will be the ‘go to’ texts for basic reference to Cp-theory. This second volume, Special Features of Function Spaces, gives a reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing  500 carefully selected problems and exercises with complete solutions. Bonus results and open problems are also given. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level.

The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. This second volume continues from the first, and can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists working in Cp-theory and related topics.  Additionally, the material can also be considered as an introduction to advanced set theory and descriptive set theory, presenting diverse topics of the theory of function spaces with the topology of pointwise convergence, or Cp-theory which exists at the intersection of topological algebra, functional analysis and general topology.

From the Reviews of Topological and Function Spaces: “…It is designed to bring a dedicated reader from the basic topological principles to the frontiers of modern research. Any reasonable course in calculus covers everything needed to understand this book. This volume can also be used as a reference for mathematicians working in or outside the field of topology (functional analysis) wanting to use results or methods of Cp-theory...On the whole, the book provides a useful addition to the literature on Cp-theory, especially at the instructional level." (Mathematical Reviews)


additional axioms of ZFC cardinal functions duality theorem function spaces pointwise convergence set theory

Authors and affiliations

  1. 1.Departamento de MatematicasUniversidad Autonoma Metropolitana-IztapIztapalapaMexico

About the authors

Vladimir V. Tkachuk is a professor in the Department of Mathematics of Autonomous Metropolitan University in Mexico City. He holds a PhD from Moscow State University and is the author of "A Cp-Theory Problem Book: Topological and Function Spaces" (Springer, 2011).

Bibliographic information

  • Book Title A Cp-Theory Problem Book
  • Book Subtitle Special Features of Function Spaces
  • Authors Vladimir V. Tkachuk
  • Series Title Problem Books in Mathematics
  • Series Abbreviated Title Problem Books Mathematics
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-04746-1
  • Softcover ISBN 978-3-319-37794-0
  • eBook ISBN 978-3-319-04747-8
  • Series ISSN 0941-3502
  • Edition Number 1
  • Number of Pages XIV, 583
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Topology
    Mathematical Logic and Foundations
    Functional Analysis
  • Buy this book on publisher's site


“This is a well-written and very interesting book from several points of view and can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists working in Cp-theory and related topics. … I hope that this book becomes the right hand of students and researchers in mathematics.” (Dimitrios N. Georgiou, Mathematical Reviews, May, 2015)

“This volume, devoted to special properties of function spaces, is divided into four chapters … . The concise beginning of each section contains definitions of topics used in that section. … this problem book will become one of the table books for all researchers interested in Cp-theory and its relations with other fields of mathematics.” (Ljubiša D. Kočinac, zbMATH, Vol. 1303, 2015)