General Topology Course
This course covers essential concepts in general topology, including topological spaces, compactness, connectedness, Hausdorff properties, homotopy, and fundamental groups. Participants will develop skills in writing clear, rigorous proofs suitable for advanced mathematical research and professional applications.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
This General Topology Course provides a focused, practical journey from basic topological spaces and standard constructions to compactness, connectedness, and separation axioms. You will work with homeomorphisms, homotopy, deformation retracts, and fundamental group concepts, learning to distinguish spaces using invariants, covering spaces, quotients, and rigorous written proofs.
Elevify advantages
Develop skills
- Master core topological spaces: construct, compare, and classify them rigorously.
- Analyse compactness, connectedness, and separation axioms using concise proofs.
- Employ homotopy, deformation retracts, and CW complexes to simplify spaces.
- Apply fundamental groups and covering spaces to distinguish non-homeomorphic spaces.
- Craft precise, research-level topological proofs from geometric intuition.
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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