A Guide to Topology /

A Guide to Topology is an introduction to basic topology. It covers point-set topology as well as Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, an...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Krantz, Steven G. (Steven George), 1951-
Format: Electronic eBook
Language:Inglés
Published: Cambridge : Cambridge University Press, 2012.
Series:Dolciani mathematical expositions.
Subjects:
Topology.
Topologie.
MATHEMATICS > Topology.
Topology
Online Access:Texto completo
Table of Contents:
  • Preface
  • Contents
  • 1 Fundamentals
  • 1.1 What is Topology?
  • 1.2 First Definitions
  • 1.3 Mappings
  • 1.4 The Separation Axioms
  • 1.5 Compactness
  • 1.6 Homeomorphisms
  • 1.7 Connectedness
  • 1.8 Path-Connectedness
  • 1.9 Continua
  • 1.10 Totally Disconnected Spaces
  • 1.11 The Cantor Set
  • 1.12 Metric Spaces
  • 1.13 Metrizability
  • 1.14 Baireâ€?s Theorem
  • 1.15 Lebesgueâ€?s Lemma and Lebesgue Numbers
  • 2 Advanced Properties of Topological Spaces
  • 2.1 Basis and Subbasis
  • 2.2 Product Spaces
  • 2.3 Relative Topology
  • 2.4 First Countable, Second Countable, and So Forth2.5 Compactifications
  • 2.6 Quotient Topologies
  • 2.7 Uniformities
  • 2.8 Morse Theory
  • 2.9 Proper Mappings
  • 2.10 Paracompactness
  • 3 Moore-Smith Convergence and Nets
  • 3.1 Introductory Remarks
  • 3.2 Nets
  • 4 Function Spaces
  • 4.1 Preliminary Ideas
  • 4.2 The Topology of Pointwise Convergence
  • 4.3 The Compact-Open Topology
  • 4.4 Uniform Convergence
  • 4.5 Equicontinuity and the Ascoli-Arzela Theorem
  • 4.6 The Weierstrass Approximation Theorem
  • Table of Notation
  • Glossary

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