# Topology by James Munkres | Prerequisites, Level & TOC

• Topology
• micromass
In summary, "Topology" by James Munkres is an excellent textbook that provides a solid foundation in general topology and a taste of algebraic topology. It is well-written and expository, with a thorough coverage of topics such as set theory, functions, topological spaces, connectedness, compactness, separation axioms, and more. The only potential weakness is that some sections on metric topology may be tedious without a recent course in analysis, but this can be remedied by supplementing with other resources. Overall, this book is highly recommended for undergraduate students with a background in rigorous mathematics.

## For those who have used this book

• ### Lightly don't Recommend

• Total voters
8
micromass
Staff Emeritus
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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]

Last edited by a moderator:
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.

## 1. What are the prerequisites for studying Topology by James Munkres?

The prerequisites for studying Topology by James Munkres are a strong understanding of basic mathematics including set theory, real analysis, and linear algebra. It is also helpful to have some familiarity with abstract algebra and topology concepts such as open and closed sets, continuity, and compactness.

## 2. Is Topology by James Munkres suitable for beginners?

No, Topology by James Munkres is not suitable for beginners. It is a graduate-level textbook and assumes a strong foundation in mathematics.

## 3. What level of mathematics is required to understand Topology by James Munkres?

Topology by James Munkres is a graduate-level textbook and requires a high level of mathematical understanding. This includes a strong background in areas such as set theory, real analysis, and linear algebra.

## 4. What topics are covered in Topology by James Munkres?

Topology by James Munkres covers a wide range of topics in topology, including point-set topology, topological spaces, continuity, connectedness, compactness, and separation axioms. It also covers more advanced topics such as the fundamental group, homotopy, and homology.

## 5. Is Topology by James Munkres a good resource for self-study?

Yes, Topology by James Munkres is often used as a textbook for self-study in topology. It is well-structured and includes many examples and exercises to help reinforce the concepts. However, it is recommended to have some background in mathematics before attempting to study it on your own.

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