General Topology Course
Gain mastery in general topology essentials like topological spaces, compactness, connectedness, Hausdorff properties, homotopy, and fundamental groups. Develop skills to write precise, rigorous proofs for advanced maths research and professional applications.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course offers a practical journey from basic topological spaces and key constructions to compactness, connectedness, and separation axioms. Practice with homeomorphisms, homotopy, deformation retracts, and fundamental group concepts. Learn to classify spaces using invariants, covering spaces, quotients, and write solid, rigorous proofs.
Elevify advantages
Develop skills
- Master key topological spaces: construct, compare, and classify them rigorously.
- Analyse compactness, connectedness, and separation axioms with quick, precise proofs.
- Apply homotopy, deformation retracts, and CW complexes to simplify spaces.
- Use fundamental groups and covering spaces to tell apart non-homeomorphic spaces.
- Craft clear, research-level proofs from geometric intuition.
Suggested summary
Before starting, you can change the chapters and 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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