Topology I

Munkres

Topology I (Munkres, Milnor)

1. (Set Theory and Logic)

2. Topological Spaces and Continuous Functions

3. Connectedness and Compactness

4. Countability and Separation Axioms

5. The Tychonoff Theorem

6. Metrization Theorems and Paracompactness

7. Complete Metric Spaces and Function Spaces

8. Baire Spaces and Dimension Theory

9. Sard theorem

10. Brouwer fixed point theorem

11. Borsuk-Ulam theorem

12. Poincare-Hopf theorem

Other materials:

Topology of curves

• Whitney-Grauenstein Theorem

• Thm: Simple Jordan curve has enroul one.

• Four-vertices theorem