Topology by Munkres

• Topology

• Total voters
8

Main Question or Discussion Point

Code:
[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 $X\times Y$
[*] 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 $S^n[/itex [*] Fundamental Groups of Some Surfaces [/LIST] [*] Separation Theorems in the Plane [LIST] [*] The Jordan Separation Theorem [*] Invariance of Domain [*] The Jordan Curve Theorem [*] Embedding Graphs in the Plane [*] The Winding Number of a Simple Closed Curve [*] The Cauchy Integral Formula [/LIST] [*] The Seifert-van Kampen Theorem [LIST] [*] Direct Sums of Abelian Groups [*] Free Products of Groups [*] Free Groups [*] The Seifert-van Kampen Theorem [*] The Fundamental Group of a Wedge of Circles [*] Adjoining a Two-cell [*] The Fundamental Groups of the Torus and the Dunce Cap [/LIST] [*] Classification of surfaces [LIST] [*] Fundamental Groups of Surfaces [*] Homology of Surfaces [*] Cutting and Pasting [*] The Classification Theorem [*] Constructing Compact Surfaces [/LIST] [*] Classification of Covering Spacs [LIST] [*] Equivalence of Covering Spaces [*] The Universal Covering Space [*] Covering Transformations [*] Existence of Covering Spaces [*] Supplementary Exercises: Topological Properties and [itex]\pi_1$
[/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]

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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.