A Cp-Theory Problem Book

The theory of function spaces endowed with the topology of pointwise 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

Preface.- Introduction.- 1.1. Basic notions of topology and function spacesBibliographic notes.- 1.2. Solutions of problems 1.001-1.500.- 1.3. Bonus results: some hidden statements.- 1.4. Open problems.- 1.5. Bibliography.- 1.6. List of special symbols.- 1.7. Index.