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Introduction To Topology 3RD Edition

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Introduction To Topology 3RD Edition Cover

 

Synopses & Reviews

Publisher Comments:

Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

Synopsis:

Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Synopsis:

An undergraduate introduction to the fundamentals of topology — engagingly written, filled with helpful insights, complete with many stimulating and imaginative exercises to help students develop a solid grasp of the subject.

Description:

Includes bibliographical references (p. 201-202) and index.

Table of Contents

Preface

1 Theory of Sets

  1 Introduction

  2 Sets and subsets

  3 "Set operations: union, intersection, and complement"

  4 Indexed families of sets

  5 Products of sets

  6 Functions

  7 Relations

  8 Composition of functions and diagrams

  9 "Inverse functions, extensions, and restrictions"

  10 Arbitrary products

2 Metric Spaces

  1 Introduction

  2 Metric spaces

  3 Continuity

  4 Open balls and neighborhoods

  5 Limits

  6 Open sets and closed sets

  7 Subspaces and equivalence of metric spaces

  8 An infinite dimensional Euclidean space

3 Topological Spaces

  1 Introduction

  2 Topological spaces

  3 Neighborhoods and neighborhood spaces

  4 "Closure, interior, boundary"

  5 "Functions, continuity, homeomorphism"

  6 Subspaces

  7 Products

  8 Identification topologies

  9 Categories and functors

4 Connectedness

  1 Introduction

  2 Connectedness

  3 Connectedness on the real line

  4 Some applications of connectedness

  5 Components and local connectedness

  6 Path-connected topological spaces

  7 Homotopic paths and the fundamental group

  8 Simple connectedness

5 Compactness

  1 Introduction

  2 Compact topological spaces

  3 Compact subsets of the real line

  4 Products of compact spaces

  5 Compact metric spaces

  6 Compactness and the Bolzano-Weierstrass property

  7 Surfaces by identification

Bibliography

Index

Product Details

ISBN:
9780486663524
Author:
Mendelson, Bert
Publisher:
Dover Publications
Author:
Mathematics
Location:
New York :
Subject:
General
Subject:
Geometry - General
Subject:
Topology
Subject:
General Mathematics
Subject:
Mathematics-Geometry and Trigonometry
Subject:
Set Theory
Subject:
Metric spaces
Edition Number:
3
Edition Description:
Third Edition
Series:
Dover Books on Mathematics
Series Volume:
TM 11-1520-236-34P
Publication Date:
19900731
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
224
Dimensions:
8.5 x 5.38 in 0.55 lb

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Related Subjects


Science and Mathematics » Chemistry » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Calculus » Precalculus
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Modeling
Science and Mathematics » Mathematics » Topology

Introduction To Topology 3RD Edition New Trade Paper
0 stars - 0 reviews
$12.95 In Stock
Product details 224 pages Dover Publications - English 9780486663524 Reviews:
"Synopsis" by ,
Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.
"Synopsis" by ,
An undergraduate introduction to the fundamentals of topology — engagingly written, filled with helpful insights, complete with many stimulating and imaginative exercises to help students develop a solid grasp of the subject.

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