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 future research
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.
Detailed summary of exercise sectionsPreface Introduction 1.1. 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 convergence 1.1.3. Metrizability and completeness1.1.4. Compactness type properties in function spaces 1.1.5. More on completeness. Realcompact spaces Bibliographic notes 1.2. Solutions of problems 1.001–1.500 1.3. Bonus results: some hidden statements1.3.1. Standard spaces 1.3.2. 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 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 Cp-spaces 1.4.7. Very general questions 1.4.8. Fuzzy questions1.4.9. Naïve questions 1.4.10. Raznoie (unclassified questions)1.5. Bibliography1.6. List of special symbols1.7. Index
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.
From the reviews:
"This is a well-written and very interesting book from several points of view. It is designed for mathematicians who are dealing with Cp-theory for the first time but also for mathematicians with very good knowledge of the subject. It is designed to bring a dedicated reader from the basic topological principles to the frontiers of modern research. Any reasonable course in calculus covers everything needed to understand this book. This volume can also be used as a reference for mathematicians working in or outside the field of topology (functional analysis) wanting to use results or methods of Cp-thoery...On the whole, the book provides a useful addition to the literature on Cp-theory, especially at the instructional level." (Dimitrios N. Georgiou, Mathematical Reviews)
"A guidebook for the reader to reach the frontiers of this field as of 2010 without first having to master a large amount of general topology. ... A detailed summary of exercises divides each basic notion into a number of topics. ... The Bibliography and Index are adequate for a reader working his way through the book ... . This book is a welcome addition to the field of general topology and Cp-theory in particular.” (James V. Whittaker, Zentralblatt MATH, Vol. 1222, 2011)
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.
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.
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.
From the reviews:
"This is a well-written and very interesting book from several points of view. It is designed for mathematicians who are dealing with Cp-theory for the first time but also for mathematicians with very good knowledge of the subject. It is designed to bring a dedicated reader from the basic topological principles to the frontiers of modern research. Any reasonable course in calculus covers everything needed to understand this book. This volume can also be used as a reference for mathematicians working in or outside the field of topology (functional analysis) wanting to use results or methods of Cp-thoery...On the whole, the book provides a useful addition to the literature on Cp-theory, especially at the instructional level." (Dimitrios N. Georgiou, Mathematical Reviews)
"A guidebook for the reader to reach the frontiers of this field as of 2010 without first having to master a large amount of general topology. ... A detailed summary of exercises divides each basic notion into a number of topics. ... The Bibliography and Index are adequate for a reader working his way through the book ... . This book is a welcome addition to the field of general topology and Cp-theory in particular." (James V. Whittaker, Zentralblatt MATH, Vol. 1222, 2011)
Inhaltsverzeichnis
Detailed 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 1.001¿1.500
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 Cp-spaces
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
Klappentext
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
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Detailed solutions to each of the presented problems and exercises
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A comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory
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Numerous open problems and directions for future research
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Includes supplementary material: sn.pub/extras
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