University Mathematics
Topology
Point-set topology: open sets, continuity, compactness and connectedness in their most general setting.
Curriculum / Syllabus
- Topological Spaces, Bases and Subspaces
- Metric Spaces
- Continuous Functions and Homeomorphisms
- Product and Quotient Topologies
- Connectedness and Path-Connectedness
- Compactness
- Countability and Separation Axioms
Exam & Course Strategy
Topology exams consist almost entirely of proofs and counterexamples. We collect the key examples (the cofinite, lower limit, product and box topologies) that settle most true-or-false questions.