Topology Course
This course builds mastery in core topology concepts including topological spaces, continuity, compactness, homotopy, and fundamental groups. Learners will apply invariants to differentiate shapes, examine dynamical systems, and produce clear, rigorous proofs ideal for advanced mathematical pursuits and research endeavours.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Gain expertise in topological spaces, continuity, compactness, separation axioms, progressing to homotopy, deformation retracts, homotopy equivalence, fundamental groups, covering spaces, and invariants, with skills to select tools aptly 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 efficiently.
- Compute fundamental groups and distinguish spaces using algebraic invariants.
- Analyse homotopy, deformation retracts to identify holes, contractibility, and equivalence.
- Develop research-level proof writing skills with concise 10–20 line arguments 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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