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Topology Course

Topology Course
from 4 to 360h flexible workload
certificate valid in your country

What will I learn?

This Topology Course offers a focused path to mastering topological spaces, continuity, compactness, and separation axioms, then moves quickly to homotopy, deformation retracts, and homotopy equivalence. You will work with fundamental groups, covering spaces, and key invariants, learn when to use each tool, and practice writing concise, rigorous reports suitable for advanced projects and research-level work.

Elevify advantages

Develop skills

  • Master topological spaces: build, compare, and classify spaces with rigor.
  • Apply compactness and continuity: prove key theorems and homeomorphism tests fast.
  • Use fundamental groups: compute π1 and distinguish spaces via algebraic invariants.
  • Analyze homotopy and deformation: detect holes, contractibility, and equivalence.
  • Write research-level proofs: 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.
Workload: between 4 and 360 hours

What our students say

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Very great course. Lots of rich information.
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