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Here are the solutions to MunkresTopology. Obviously, it is currently incomplete. I am working on getting the rest finished and uploaded. I frequently look back on my own solutions, realize they are wrong, and subsequently wonder how I could have ever thought they were correct; hence, if there are any confusing statements or incomplete solutions that may have been overlooked, please leave a comment or contact me so that I may either correct the solution or add some clarity.
- Chapter 1 Set Theory and Logic
- 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 Topological Spaces and Continuous Functions
- Section 12: Topological Spaces
- Section 13: Basis for a Topology
- Section 14: The Order Topology
- Section 15: The Product Topology onX×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 Connectedness and Compactness
- 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 Countability and Separation Axioms
- 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 5 The Tychonoff Theorem
- Section 37: The Tychonoff Theorem
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