A Cp-Theory Problem Book Topological and Function Spaces [Hardcover]

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.

Through carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By introducing each of the major topics in Cp-theory, the volume reflects the state-of-the-art in modern Cp-theory.

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 1.0011.5001.3. Bonlc%