Munkres (2000) Topology with Solutions

Below are links to answers and solutions for exercises in the Munkres (2000) Topology, Second Edition.

• Chapter 1

  • Section 1: Fundamental Concepts
  • Section 2: Functions
  • Section 3: Relations
  • Section 4: The Integers and the Real Numbers
  • Section 5: Cartesian Products
  • Section 6: Finite Sets
  • Section 7: Countable and Uncountable Sets
  • Section 8*: The Principle of Recursive Definition
  • Section 9: Infinite Sets and the Axiom of Choice
  • Section 10: Well-Ordered Sets
  • Section 11*: The Maximum Principle
  • Supplementary Exercises*: Well-Ordering

• Chapter 2

  • Section 12: Topological Spaces
  • Section 13: Basis for a Topology
  • Section 14: The Order Topology
  • Section 15: The Product Topology on X×Y
  • Section 16: The Subspace Topology
  • Section 17: Closed Sets and Limit Points
  • Section 18: Continuous Functions
  • Section 19: The Product Topology
  • Section 20: The Metric Topology
  • Section 21: The Metric Topology (continued)
  • Section 22*: The Quotient Topology
  • Supplementary Exercises*: Topological Groups

• Chapter 3

  • Section 23: Connected Spaces
  • Section 24 Connected Subspaces of the Real Line
  • Section 25*: Components and Local Connectedness
  • Section 26: Compact Spaces
  • Section 27: Compact Subspaces of the Real Line
  • Section 28: Limit Point Compactness
  • Section 29: Local Compactness
  • Supplementary Exercises*: Nets

• Chapter 4

  • Section 30: The Countability Axioms
  • Section 31: The Separation Axioms
  • Section 32: Normal Spaces
  • Section 33: The Urysohn Lemma
  • Section 34: The Urysohn Metrization Theorem
  • Section 35*: The Tietze Extension Theorem
  • Section 36*: Imbeddings of Manifolds
  • Supplementary Exercises*: Review of the Basics

• Chapter 9

  • Section 51: Homotopy of Paths
  • Section 52: The Fundamental Group
  • Section 53: Covering Spaces
  • Section 54: The Fundamental Group of the Circle
  • Section 55: Retractions and Fixed Points
  • Section 56: The Fundamental Theorem of Algebra

• Chapter 11

  • Section 67: Direct Sums of Abelian Groups

Enjoy!