General Topology Course
This course teaches the essentials of general topology, including topological spaces, compactness, connectedness, Hausdorff properties, homotopy, and fundamental groups. Students learn to craft rigorous proofs that prepare them for advanced math research and professional careers, with hands-on practice in classifying spaces and using invariants.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course provides a practical journey through general topology, starting from basic spaces and constructions to key concepts like compactness, connectedness, and separation axioms. Learners will work with homeomorphisms, homotopy, deformation retracts, fundamental groups, covering spaces, and quotients, gaining skills to distinguish spaces using invariants and write rigorous proofs.
Elevify advantages
Develop skills
- Master key topological spaces by building, comparing, and classifying them rigorously.
- Analyze compactness, connectedness, and separation using quick, precise proofs.
- Apply homotopy, deformation retracts, and CW complexes to simplify spaces.
- Use fundamental groups and covering spaces to tell non-homeomorphic spaces apart.
- Write clear, precise topological proofs ready for research 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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