A Cp-Theory Problem Book: Compactness in Function Spaces

ISBN-13: 9783319365367 / Angielski / Miękka / 2016 / 524 str.

Vladimir V. Tkachuk

Opis

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 (c) 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 (c) 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.

Recenzje

"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." (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)

Spis treści

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.

O autorze

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: Special Features of Function Spaces (Springer, 2014) and A Cp-Theory Problem Book: Topological and Function Spaces (Springer, 2011). Both volumes have published in the Problem Books in Mathematics series.

Blurb

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.