A Cp-Theory Problem Book: Topological and Function Spaces
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.
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apply Fact apply Problem arbitrary space Arhangel’skii assume Baire space base cardinal Čech-complete clopen closed discrete closed subsets closed subspace collectionwise normal compact subspace conclude consequence continuous function continuous map converges defined dense subspace discrete space disjoint family elements embeds f is continuous Fact1 fe C,(X following properties function f G-compact Given Go-set hereditarily homeomorphic i e o implies infinite intersection Let f Lindel€of Lindelöf Lindelöf space linear locally finite map f metric space metrizable n e a n e o natural projection non-empty open Observe open cover open neighbourhood open set open subsets paracompact Proof pseudocompact space realcompact space second countable space separates the points sequence set F solution is complete space C,(X T-base topological space topology Tychonoff space U O V ultrafilter uncountable