Lecture(s)   |
Sections (approximately)     |
Comments/Topics |
1 |
1.2, 1.3 |
Sets, operations on sets |
1 |
1.4, 1.5 |
Indexed families of sets, arbitrary unions and products |
1 |
1.6, 1.7 |
Functions, relations |
1 |
2.1, 2.2 |
Metric spaces |
1 |
2.3 |
Continuity |
1 |
2.4 |
Open balls |
1 | 2.5 | Limits |
1 |
2.6, 2.7 |
Open sets, closed sets, subsets, equivalence |
1 |
3.2 |
Topological spaces |
1 | Munkres | Basis of a topology |
1 |
Munkres |
Closure, interior, boundary |
1 | 3.6 | Subspaces |
1 |
3.5 |
Functions, continuity, homeomorphism |
1 |
3.7 |
Products |
1 | Halloween Lecture | Scary topologies |
1 |
3.8 |
Quotient topologies |
1 |
4.2, 4.3 |
Connectedness, connectedness of the real line |
1 |
4.5, 4.6 |
Components, path connectedness, contractibility |
1 |
5.2 |
Compactness |
1 |
5.3 |
Compact subsets of the real line |
1 |
5.4 |
Products of compact spaces |
1 |
5.5 |
Compact metric spaces |
1 |
various |
Heine Borel Theorem |
various |
various |
Surfaces |
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