Exam syllabus/curriculum

This is the planned exam syllabus.  Dates (day/month) will show when the material is first discussed.

• Section 1: Fundamental Concepts (20/8)
• Section 2: Functions (21/8)
• Section 3: Relations (up to Order Relations)
• Section 5. Cartesian Products (21/8)
• Section 6: Finite Sets (21/8)
• Section 7: Countable and Uncountable Sets (18/9)
• Section 12: Topological Spaces (27/8)
• Section 13: Basis for a Topology (27/8)
• Section 15: The Product Topology on X x Y (3/9)
• Section 16: The Subspace Topology (3/9)
• Section 17: Closed Sets and Limit Points (4/9)
• Section 18: Continuous Functions (10/9)
• Section 19: The Product Topology (18/9)
• Section 20: The Metric Topology (24/9)
• 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 (without proof)
• Section 36: Embeddings of Manifolds
• Section 37: The Tychonoff Theorem (without proof)
• Section 43: Complete Metric Spaces
• Section 45: Compactness in Metric Spaces
• Section 46: Pointwise and Compact Convergence
• 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