Week 2 Synthesis
Central Question
Can I explain why open sets, gluing, deformation and algebraic invariants belong to the same story?
Why This Matters
A coherent topological mental model should explain both familiar examples and the places where geometric intuition becomes unreliable.
Learning Prompt
Consolidate metric spaces → open sets → topology → continuity → homeomorphism → connectedness → compactness → quotient spaces → homotopy → fundamental group → algebraic topology. Ask substantial conceptual questions and identify weaknesses in my mental model.
Ideas
Examples
Questions
Connections
- Continuity Without Epsilon-Delta
- Compactness
- Quotient Spaces
- Fundamental Group
- From Surfaces to Manifolds
- Week overview