A Cp-Theory Problem Book

The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from each of these areas of research.Through over 500 carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research.Key features include: A unique problem-based introduction to the theory of function spaces. Detailed solutions to each of the presented problems and exercises. A comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory. Numerous open problems and directions for further research.This volume can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists studying Cp-theory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research.

A unique problem-based introduction to the theory of function spaces

Detailed summary of exercise sectionsPrefaceIntroduction1.1. Basic notions of topology and function spaces1.1.1. Topologies, axioms of separation and a glance at Cp(X)1.1.2. Products, cardinal functions and convergence1.1.3. Metrizability and completeness1.1.4. Compactness type properties in function spaces1.1.5. More on completeness. Realcompact spacesBibliographic notes1.2. Solutions of problems 1.001¿1.5001.3. Bonus results: some hidden statements1.3.1. Standard spaces1.3.2. Metrizable spaces and compact spaces1.3.3. Properties of continuous maps1.3.4. Covering properties, normality and open families1.3.5. Product spaces and cardinal invariants1.3.6. Raznoie (unclassified results)1.4. Open problems1.4.1. Local properties1.4.2. Discreteness of X and completeness of Cp(X)1.4.3. Dense subspaces1.4.4. The Lindelöf property in X and Cp(X)1.4.5. Other covering properties1.4.6. Mappings which involve Cp-spaces1.4.7. Very general questions1.4.8. Fuzzy questions1.4.9. Naïve questions1.4.10. Raznoie (unclassified questions)1.5. Bibliography1.6. List of special symbols1.7. Index