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Topology / James R. Munkres.
Author
Munkres, James R., 1930-
[Browse]
Format
Book
Language
English
Εdition
2nd ed.
Published/Created
Upper Saddle River, NJ : Prentice Hall, Inc., ©2000.
Description
xvi, 537 pages : illustrations ; 25 cm
Availability
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA611 .M82 2000
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Lewis Library - Stacks
QA611 .M82 2000
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Lewis Library - Stacks
QA611 .M82 2000
Browse related items
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Lewis Library - Stacks
QA611 .M82 2000
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Details
Subject(s)
Topology
[Browse]
Summary note
This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures.
Bibliographic references
Includes bibliographical references (p. 517-518) and index.
Contents
General topology : Set theory and logic : Fundamental concepts ; Functions ; Relations ; The integers and the real numbers ; Cartesian products ; Finite sets ; Countable and uncountable sets ; The principle of recursive definition ; Infinite sets and the axiom of choice ; Well-ordered sets ; The maximum principle
Topological spaces and continuous functions : Topological spaces ; Basis for a topology ; The order topology ; The product topology on X x Y ; The subspace topology ; Closed sets and limit points ; Continuous functions ; The product topology ; The metric topology ; The metric topology (continued) ; The quotient topology
Connectedness and compactness : Connected spaces ; Connected subspaces of the real line ; Components and local connectedness ; Compact spaces ; Compact subspaces of the real line ; Limit point compactness ; Local compactness
Countability and separation axioms : The countability axioms ; The separation axioms ; Normal spaces ; The Urysohn lemma ; The Urysohn metrization theorem ; The Tietze extension theorem ; Imbeddings of manifolds
Tychonoff theorem : The Tychonoff theorem ; The stone-Cech compactification
Metrization theorems and paracompactness : Local finiteness ; The Nagata-Smirnov metrization theorem ; Paracompactness ; The Smirnov metrization theorem
Complete metric spaces and function spaces : Complete metric spaces ; A space-filling curve ; Compactness in metric spaces ; Pointwise and compact convergence ; Ascoli’s theorem
Baire spaces and dimension theory : Baire spaces ; A nowhere-differentiable function ; Introduction to dimension theory
Algebraic topology : The fundamental group : Homotopy of paths ; The fundamental group ; Covering spaces ; The fundamental group of the circle ; Retractions and fixed points ; The fundamental theorem of algebra ; The Borsuk-Ulam theorem ; Deformation retracts and homotopy type ; The fundamental group of () ; Fundamental groups of some surfaces
Separation theorems in the plane : The Jordan separation theorem ; Invariance of domain ; The Jordan curve theorem ; Imbedding graphs in the plane ; The winding number of a simple closed curve ; The Cauchy integral formula
The Seifert-van Kampen theorem : Direct sums of abelian groups ; Free products of groups ; Free groups ; The Seifert-van Kampen theorem ; The fundamental group of a wedge of circles ; Adjoining a two-cell ; The fundamental groups of the torus and the dunce cap
Classification of surfaces : Fundamental groups of surfaces ; Homology of surfaces ; Cutting and pasting ; The classification theorem ; Constructing compact surfaces
Classification of covering spaces : Equivalence of covering spaces ; The universal covering space ; Covering transformations ; Existence of covering spaces
Applications to group theory : Covering spaces of a graph ; The fundamental group of a graph ; Subgroups of free groups.
Show 11 more Contents items
ISBN
0131816292 ((case))
9780131816299 ((case))
0131784498
9780131784499
LCCN
99052942
OCLC
42683260
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