Foundations of General Topology

Foundations of General Topology

1st Edition - January 1, 1964

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  • Author: William J. Pervin
  • eBook ISBN: 9781483225159

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Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction. This book provides a careful treatment of general topology. Organized into 11 chapters, this book begins with an overview of the important notions about cardinal and ordinal numbers. This text then presents the fundamentals of general topology in logical order processing from the most general case of a topological space to the restrictive case of a complete metric space. Other chapters consider a general method for completing a metric space that is applicable to the rationals and present the sufficient conditions for metrizability. This book discusses as well the study of spaces of real-valued continuous functions. The final chapter deals with uniform continuity of functions, which involves finding a distance that satisfies certain requirements for all points of the space simultaneously. This book is a valuable resource for students and research workers.

Table of Contents

  • Preface

    Chapter 1 Algebra of Sets

    1.1 Sets and Subsets

    1.2 Operations on Sets

    1.3 Relations

    1.4 Mappings

    1.5 Partial Orders

    Chapter 2 Cardinal and Ordinal Numbers

    2.1 Equipotent Sets

    2.2 Cardinal Numbers

    2.3 Order Types

    2.4 Ordinal Numbers

    2.5 Axiom of Choice

    Chapter 3 Topological Spaces


    3.1 Open Sets and Limit Points

    3.2 Closed Sets and Closure

    3.3 Operators and Neighborhoods

    3.4 Bases and Relative Topologies

    Chapter 4 Connectedness, Compactness, and Continuity

    4.1 Connected Sets and Components

    4.2 Compact and Countably Compact Spaces

    4.3 Continuous Functions

    4.4 Homeomorphisms

    4.5 Arcwise Connectivity

    Chapter 5 Separation and Countability Axioms

    5.1 T0- and T1-Spaces

    5.2 T2-Spaces and Sequences

    5.3 Axioms of Countability

    5.4 Separability and Summary

    5.5 Regular and Normal Spaces

    5.6 Completely Regular Spaces

    Chapter 6 Metric Spaces

    6.1 Metric Spaces as Topological Spaces

    6.2 Topological Properties

    6.3 Hilbert (l2) Space

    6.4 Fréchet Space

    6.5 Space of Continuous Functions

    Chapter 7 Complete Metric Spaces

    7.1 Cauchy Sequences

    7.2 Completions

    7.3 Equivalent Conditions

    7.4 Baire Theorem

    Chapter 8 Product Spaces

    8.1 Finite Products

    8.2 Product Invariant Properties

    8.3 Metric Products

    8.4 Tichonov Topology

    8.5 Tichonov Theorem

    Chapter 9 Function and Quotient Spaces

    9.1 Topology of Pointwise Convergence

    9.2 Topology of Compact Convergence

    9.3 Quotient Topology

    Chapter 10 Metrization and Paracompactness

    10.1 Urysohn's Metrization Theorem

    10.2 Paracompact Spaces

    10.3 Nagata-Smirnov Metrization Theorem

    Chapter 11 Uniform Spaces

    11.1 Quasi Uniformization

    11.2 Uniformization

    11.3 Uniform Continuity

    11.4 Completeness and Compactness

    11.5 Proximity Spaces



Product details

  • No. of pages: 222
  • Language: English
  • Copyright: © Academic Press 1964
  • Published: January 1, 1964
  • Imprint: Academic Press
  • eBook ISBN: 9781483225159

About the Author

William J. Pervin

About the Editor

Ralph P. Boas

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