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A Cp-Theory Problem Book: Topological and Function Spaces (Problem Books in Mathematics)

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A Cp-Theory Problem Book: Topological and Function Spaces (Problem Books in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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.

Synopsis:

This book is a self-contained introduction to the theory of function spaces endowed with the topology of pointwise convergence. It covers many popular topics in Cp-theory 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 Cp-theory 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 Contents

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

Product Details

ISBN:
9781441974419
Author:
Tkachuk, Vladimir V.
Publisher:
Springer
Author:
Tkachuk, Vladimir
Subject:
Topology - General
Subject:
Topology
Subject:
C_p-theory
Subject:
General Topology
Subject:
point-set topology
Subject:
Compactness
Subject:
Function spaces.
Subject:
metrizability
Subject:
open problems
Subject:
pointwise convergence
Subject:
Algebraic topology
Subject:
Manifolds and Cell Complexes (incl. Diff.Topology)
Subject:
Manifolds and Cell Complexes (incl. Diff.Topology) 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 mode
Subject:
MATHEMATICS / Topology
Copyright:
Edition Description:
2011
Series:
Problem Books in Mathematics
Publication Date:
20110205
Binding:
HARDCOVER
Language:
English
Pages:
504
Dimensions:
235 x 155 mm

Related Subjects


Science and Mathematics » Astronomy » General
Science and Mathematics » Mathematics » Topology

A Cp-Theory Problem Book: Topological and Function Spaces (Problem Books in Mathematics) New Hardcover
0 stars - 0 reviews
$84.95 In Stock
Product details 504 pages Springer - English 9781441974419 Reviews:
"Synopsis" by , 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.
"Synopsis" by , This book is a self-contained introduction to the theory of function spaces endowed with the topology of pointwise convergence. It covers many popular topics in Cp-theory 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 Cp-theory 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.
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