Topology Course
This course builds expertise in core topology concepts like topological spaces, continuity, compactness, separation axioms, homotopy, deformation retracts, fundamental groups, and covering spaces. Learners will master key invariants to differentiate shapes, analyse dynamical systems, and produce clear, rigorous proofs ideal for advanced mathematical projects and research.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
Gain mastery over topological spaces, continuity, compactness, separation axioms, homotopy, deformation retracts, homotopy equivalence, fundamental groups, covering spaces, and invariants. Learn to select appropriate tools and craft concise, rigorous proofs for advanced projects and research work.
Elevify advantages
Develop skills
- Master topological spaces through building, comparing, and classifying with precision.
- Apply compactness and continuity to prove theorems and test homeomorphisms efficiently.
- Compute fundamental groups and distinguish spaces using algebraic invariants.
- Analyse homotopy, deformation retracts, and equivalence to detect holes and contractibility.
- Develop skills in writing concise, research-level proofs for topology projects.
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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