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A CpTheory Problem Book: Topological and Function Spaces (Problem Books in Mathematics)by Vladimir V. Tkachuk
Synopses & ReviewsPublisher Comments:The theory of function spaces endowed with the topology of pointwise convergence, or Cptheory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology. Cptheory 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 selfcontained introduction to Cptheory and general topology. By systematically introducing each of the major topics in Cptheory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. Key features include:  A unique problembased introduction to the theory of function spaces.  Detailed solutions to each of the presented problems and exercises.  A comprehensive bibliography reflecting the stateoftheart in modern Cptheory.  Numerous open problems and directions for further research. This volume can be used as a textbook for courses in both Cptheory and general topology as well as a reference guide for specialists studying Cptheory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research.
Synopsis:Through carefully selected problems and exercises, this volume provides a selfcontained introduction to Cptheory and general topology. By introducing each of the major topics in Cptheory, the volume reflects the stateoftheart in modern Cptheory.
Synopsis:This book is a selfcontained introduction to the theory of function spaces endowed with the topology of pointwise convergence. It covers many popular topics in Cptheory and brings the reader to the frontier of modern research. This volume contains 500 problems and exercises with complete solutions. It can be used as a textbook of both Cptheory and topology. This book is the first in a four part sequence of problems books by the same author. Each book focuses on a different area of topology. Depending upon the commercial sucess of the first volume, the other three volumes may be contracted for the Problem Books in Mathematics series.
Table of ContentsDetailed summary of exercise sections Preface Introduction 1.1. Basic notions of topology and function spaces 1.1.1. Topologies, axioms of separation and a glance at Cp(X) 1.1.2. Products, cardinal functions and convergence 1.1.3. Metrizability and completeness 1.1.4. Compactness type properties in function spaces 1.1.5. More on completeness. Realcompact spaces Bibliographic notes 1.2. Solutions of problems 1.0011.500 1.3. Bonus results: some hidden statements 1.3.1. Standard spaces 1.3.2. Metrizable spaces and compact spaces 1.3.3. Properties of continuous maps 1.3.4. Covering properties, normality and open families 1.3.5. Product spaces and cardinal invariants 1.3.6. Raznoie (unclassified results) 1.4. Open problems 1.4.1. Local properties 1.4.2. Discreteness of X and completeness of Cp(X) 1.4.3. Dense subspaces 1.4.4. The Lindelöf property in X and Cp(X) 1.4.5. Other covering properties 1.4.6. Mappings which involve Cpspaces 1.4.7. Very general questions 1.4.8. Fuzzy questions 1.4.9. Naïve questions 1.4.10. Raznoie (unclassified questions) 1.5. Bibliography 1.6. List of special symbols 1.7. Index
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