Topology Course
Dive into topology essentials like spaces, continuity, compactness, homotopy, and fundamental groups. Learn to apply invariants for distinguishing shapes, examining dynamical systems, and producing clear, rigorous proofs suited for advanced mathematical pursuits and research.

from 4 to 360h flexible workload
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 gain skills to select the right tools and craft concise, rigorous reports for advanced projects and research.
Elevify advantages
Develop skills
- Master topological spaces by constructing, 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 tasks.
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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