Overview
- Discusses a wide variety of top-notch methods and results of Cp-theory and general topology presented with detailed proofs
- Serves as both an exhaustive course in Cp-theory and a reference guide for specialists in topology, set theory and functional analysis
- Includes a comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory
- Classifies 100 open problems in Cp-theory and their connections to previous research
- Includes supplementary material: sn.pub/extras
Part of the book series: Problem Books in Mathematics (PBM)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (4 chapters)
Keywords
About this book
This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. 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. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained and works in tandem with the other two, containing five hundred carefully selected problems and solutions. It 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 point wise convergence, or Cp-theory which exists at the intersection of topological algebra, functional analysis and general topology.
Reviews
“This volume … is a very useful book for all researchers working in Cp-theory (also in general topology) and its relationships with other mathematical disciplines, especially with functional analysis. The problems in chapter 4 can attract young mathematicians to work in this field and to solve some of quite difficult problems.” (Ljubiša D. Kočinac, zbMATH, Vol. 1325.54001, 2016)
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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: A Cp-Theory Problem Book
Book Subtitle: Compactness in Function Spaces
Authors: Vladimir V. Tkachuk
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-3-319-16092-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-16091-7Published: 29 June 2015
Softcover ISBN: 978-3-319-36536-7Published: 15 October 2016
eBook ISBN: 978-3-319-16092-4Published: 02 June 2015
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: XV, 524
Topics: Algebraic Topology, Functional Analysis