A Cp-Theory Problem Book: Compactness in Function Spaces by Vladimir V. TkachukA Cp-Theory Problem Book: Compactness in Function Spaces by Vladimir V. Tkachuk

A Cp-Theory Problem Book: Compactness in Function Spaces

byVladimir V. Tkachuk

Hardcover | June 29, 2015

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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.

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 ofA Cp-Theory Problem Book: Special Features of Function Spaces(Springer, 2014) andA Cp-Theory Problem Book: Topological and Function Spaces(Springer...
Title:A Cp-Theory Problem Book: Compactness in Function SpacesFormat:HardcoverDimensions:524 pagesPublished:June 29, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319160915

ISBN - 13:9783319160917


Table of Contents

Preface.- Contents.- Detailed summary of exercise sections.- Introduction.- 1. Behavior of Compactness in Function Spaces.- 2. Solutions of Problems 001-0500.- 3. Bonus Results: Some Hidden Statements.- 4. Open Problems.- Bibliography.- List of Special Symbols.- Index.

Editorial Reviews

"This volume . is a very useful book for allresearchers working in Cp-theory (also in general topology) and itsrelationships with other mathematical disciplines, especially with functionalanalysis. The problems in chapter 4 can attract young mathematicians to work inthis field and to solve some of quite difficult problems." (Ljubisa D. Kocinac,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)