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User guide
1. Some set theory
2. Metric spaces
3. Open sets
4. Basis, subbasis, subspace
5. Closed sets
6. Continuous functions
7. Connectedness
8. Path connectedness
9. Separation axioms
10. Urysohn lemma
11. Tietze extension theorem
12. Urysohn metrization theorem
13. Metrization of manifolds
14. Compact spaces
15. Heine-Borel theorem
16. Compact metric spaces
17. Tychonoff theorem
18. Compactification
19. Quotient spaces
8. Path connectedness
Notes
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Videos
Part 1 (pages 65-68)
Part 2 (pages 69-70)
Page links
Page 65: Paths in topological spaces.
Page 66: Path inverse and concatenation. Path connected spaces.
Page 67: Path connected components.
Page 68: Properties and examples of path connected components.
Page 69: Locally connected and locally path connected spaces.
Page 70: Properties of locally (path) connected spaces.
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7. Connectedness
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9. Separation axioms