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Topology Topology by Munkres

  1. Strongly Recommend

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  4. Strongly don't Recommend

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  1. Jan 19, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Preface
    [*] A Note to the  Reader
    [*] General Topology
    [LIST]
    [*] Set Theory and Logic
    [LIST]
    [*] Fundamental Concepts
    [*] Functions
    [*] Relation
    [*] 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 Choic
    [*] Well-ordered Sets
    [*] The Maximum Principle
    [*] Supplementary Exercises: Well-Ordering
    [/LIST]
    [*] Topological Spaces and Continuous Functions
    [LIST]
    [*] Topological Spaces
    [*] Basis for a Topology
    [*] The Order Topology
    [*] The Product Topology on [itex]X\times Y[/itex]
    [*] Th  Subspace Topology
    [*] Closed Sets and Limit Points
    [*] Continuous Functions
    [*] The Product Topology
    [*] The Metric Topology
    [*] The Metric Topology (continued)
    [*] The Quotient Topology
    [*] Supplementary Exercises: Topological Groups
    [/LIST]
    [*] Connectedness and Compactness
    [LIST]
    [*] 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
    [*] Supplementary Exercises: Nets
    [/LIST]
    [*] Countability and Separation Axioms
    [LIST]
    [*] The Countability Axioms
    [*] The Separation Axioms
    [*] Normal Spaces
    [*] The Urysohn Lemma
    [*] The Urysohn Metrization Theorem
    [*] The Tietze Extension Theorem
    [*] Imbeddings of Manifolds
    [*] Supplementary Exercises: Review of  the Basics
    [/LIST]
    [*] The Tychonoff Theorem
    [LIST]
    [*] The Tychonoff Theorem
    [*] The stone-cech Compactification
    [/LIST]
    [*] Metrization Theorems and Paracompactness
    [LIST]
    [*] Local Finiteness
    [*] The Nagata-Smirnov Metrization Theorem
    [*] Paracompactness
    [*] The Smirnov Metrization Theorem
    [/LIST]
    [*] Complete Metric Spaces and Function Spaces
    [LIST]
    [*] Complete Metric Spaces
    [*] A Space-Filling Curve
    [*] Compactness in Metric Spaces
    [*] Pointwise and Compact Convergence
    [*] Ascoli's Theorem
    [/LIST]
    [*] Baire Spaces and Dimension Theory
    [LIST]
    [*] Baire Spaces
    [*] A Nowhere-Differentiable Function
    [*] Introduction to Dimension Theory
    [*] Supplementary Exercises: Locally Euclidean Spaces
    [/LIST]
    [/LIST]
    [*] Algebraic Topology
    [LIST]
    [*] The Fundamental Group
    [LIST]
    [*] 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 [itex]S^n[/itex
    [*] Fundamental Groups of Some Surfaces
    [/LIST]
    [*]  Separation Theorems in the Plane
    [LIST]
    [*] The Jordan Separation Theorem
    [*] Invariance of Domain
    [*] The Jordan Curve Theorem
    [*] Embedding Graphs in the Plane
    [*] The Winding Number of a Simple Closed Curve
    [*] The Cauchy Integral Formula
    [/LIST]
    [*] The Seifert-van Kampen Theorem
    [LIST]
    [*] 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
    [/LIST]
    [*] Classification of surfaces
    [LIST]
    [*] Fundamental Groups of Surfaces
    [*] Homology of Surfaces
    [*] Cutting and Pasting
    [*] The Classification Theorem
    [*] Constructing Compact Surfaces
    [/LIST]
    [*] Classification of Covering Spacs
    [LIST]
    [*] Equivalence of Covering Spaces
    [*] The Universal Covering Space
    [*] Covering Transformations
    [*] Existence of Covering Spaces
    [*] Supplementary Exercises: Topological Properties and [itex]\pi_1[/itex]
    [/LIST]
    [*] Applications to Group Theory
    [LIST]
    [*] Covering Spaces of a Graph
    [*] The Fundamental Group of a Graph
    [*] Subgroups of Free Groups
    [/LIST]
    [/LIST]
    [*] Bibliography
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 4, 2013 #2
    This textbook is fantastic! It is well-written and very expository. The first four chapters, coupled with a few chapters from Part II (in particular chapters 9 and 11), provide you with an extremely solid foundation in general topology and a taste of algebraic topology.
    It is hard to find a weakness, but without a recent course in Analysis (I took Real Analysis 5 years ago), I would say that the two sections on the Metric Topology can be a bit tedious.To remedy this issue, I supplemented these sections with Bert Mendelson's coverage of metric spaces in his book "Introduction to Topology," which is also absolutely fantastic.
     
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