Topology Course Lecture Notes

Aisling McCluskey and Brian McMaster

Chapter 1: Fundamental Concepts

Describing Topological Spaces; Closed sets and Closure; Continuity and Homeomorphism; Additional Observations.

Chapter 2: Topological Properties

Compactness; Other Covering Conditions; Connectedness; Separability.

Chapter 3: Convergence

The Failure of Sequences; Nets - A Kind of `Super-Sequence'; First Countable Spaces - Where Sequences Suffice.

Chapter 4: Product Spaces

Constructing Products; Products and Topological Properties.

Chapter 5: Separation Axioms

T₁ Spaces; T₂ (Hausdorff) Spaces; T₃ Spaces; T_{3 1/2} Spaces; T₄ Spaces.

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Please use the Topology QA Board to ask for help with these notes, or on any other subjects in topology that you are studying.

Date Received: August, 1997