Topology Course
Dive into topology essentials like topological spaces, continuity, compactness, homotopy, and fundamental groups. Gain skills to distinguish shapes using invariants, analyse dynamical systems, and produce clear, rigorous proofs ideal for advanced mathematical pursuits and research endeavours.

flexible workload from 4 to 360h
valid certificate in your country
What will I learn?
This course guides you through mastering topological spaces, continuity, compactness, separation axioms, homotopy, deformation retracts, homotopy equivalence, fundamental groups, covering spaces, and key invariants. You'll learn to apply each tool effectively and craft concise, rigorous reports for advanced projects and research.
Elevify advantages
Develop skills
- Master topological spaces by building, comparing, and classifying them rigorously.
- Apply compactness and continuity to prove theorems and test homeomorphisms swiftly.
- Compute fundamental groups and use algebraic invariants to differentiate spaces.
- Analyse homotopy and deformation retracts to identify holes, contractibility, and equivalence.
- Develop research-level proof writing with concise 10–20 line arguments for topology projects.
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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