General Topology Course
Gain mastery in key general topology concepts including topological spaces, compactness, connectedness, Hausdorff properties, homotopy, and fundamental groups. Develop skills to produce clear, rigorous proofs suitable for advanced mathematical research and professional applications in New Zealand academic settings.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
This course provides a focused, practical journey from basic topological spaces and standard constructions to compactness, connectedness, and separation axioms. Practice with homeomorphisms, homotopy, deformation retracts, and fundamental group concepts, while distinguishing spaces using invariants, covering spaces, quotients, and rigorous written proofs.
Elevify advantages
Develop skills
- Master core topological spaces through building, comparing, and classifying with rigour.
- Analyse compactness, connectedness, and separation using sharp, efficient proofs.
- Apply homotopy, deformation retracts, and CW complexes to simplify spaces.
- Use fundamental groups and covering spaces to distinguish non-homeomorphic spaces.
- Write precise, research-level topological proofs from intuitive geometry.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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