A Cp-theory Problem Book: Compactness in Function Spaces [2015° ed.] 3319160915, 9783319160917

This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to stu

304 39 2MB

English Pages 524 [538] Year 2015

A Cp-theory Problem Book: Compactness in Function Spaces [2015° ed.]
3319160915, 9783319160917

Author / Uploaded
Vladimir V. Tkachuk

Table of contents :
Preface
Contents
Detailed Summary of Exercises
Introduction
1 Behavior of Compactness in Function Spaces
1.1 The Spaces Cp(X) for Compact and Compact-Like X
1.2 Corson Compact Spaces
1.3 More of Lindelöf Σ-Property. Gul'ko Compact Spaces
1.4 Eberlein Compact Spaces
1.5 Special Embeddings and Extension Operators
Bibliographic Notes to Chapter 1
2 Solutions of Problems 001–500
3 Bonus Results: Some Hidden Statements
3.1 Standard Spaces
3.2 Metrizable Spaces
3.3 Compact Spaces and Their Generalizations
3.4 Properties of Continuous Maps
3.5 Covering Properties, Normality and Open Families
3.6 Completeness and Convergence Properties
3.7 Ordered, Zero-Dimensional and Product Spaces
3.8 Cardinal Invariants and Set Theory
4 Open Problems
4.1 Sokolov Spaces and Corson Compact Spaces
4.2 Gul'ko Compact Spaces
4.3 Eberlein Compact Spaces
4.4 The Lindelöf Σ-Property in Cp(X)
4.5 The Lindelöf Property in X and Cp(X)
4.6 Extral and Extendial Spaces
4.7 Point-Finite Cellularity and Calibers
4.8 Grothendieck Spaces
4.9 Raznoie (Unclassified Questions)
Bibliography
List of Special Symbols
Index

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