General Topology Course
Master core ideas of general topology—topological spaces, compactness, connectedness, Hausdorff, homotopy, and fundamental groups—while learning to write clear, rigorous proofs that support advanced research and professional work in mathematics. This course provides a solid foundation for further mathematical studies.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
This General Topology Course offers a focused, hands-on path from basic topological spaces and standard constructions to compactness, connectedness, and separation axioms. You'll practise working with homeomorphisms, homotopy, deformation retracts, and intuitive fundamental group concepts, while learning to distinguish spaces using invariants, covering spaces, quotients, and clear, rigorous written arguments.
Elevify advantages
Develop skills
- Master core topological spaces: build, compare, and classify with rigor.
- Analyse compactness, connectedness, and separation via sharp, fast proofs.
- Use homotopy, deformation retracts, and CW intuition to simplify spaces.
- Apply fundamental group and covering ideas to distinguish non-homeomorphic spaces.
- Write precise, research-ready topological arguments 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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