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 Browse related items Request
    Lewis Library - Stacks QA611 .M82 2000 Browse related items Request
      Lewis Library - Stacks QA611 .M82 2000 Browse related items Request
        Lewis Library - Stacks QA611 .M82 2000 Browse related items Request

          Details

          Subject(s)
          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.
          ISBN
          • 0131816292 ((case))
          • 9780131816299 ((case))
          • 0131784498
          • 9780131784499
          LCCN
          99052942
          OCLC
          42683260
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