Exam syllabus

For the written examination you are expected to have studied the following sections of Munkres' "Topology".  This list is now final.

• 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 12: Topological Spaces
• Section 13: Basis for a Topology
• Section 15: The Product Topology on X x Y
• Section 16: The Subspace Topology
• Section 17: Closed Sets and Limit Points
• Section 18: Continuous Functions
• Section 19: The Product Topology [omit the box topology]
• Section 20: The Metric Topology
• Section 21: The Metric Topology (continued)
• Section 22: The Quotient Topology
• 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
• 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 [proof omitted]
• Section 36: Imbeddings of Manifolds
• Section 37: The Tychonoff Theorem [proof omitted]
• 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