Lecture 1: Metric spaces and their properties |
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Lecture 2: Closed sets and sequences |
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Lecture 3: Cauchy sequences and completeness |
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Lecture 4: Baire category theorem and completeness of $\mathbb R$ |
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Lecture 5: Continuity |
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Lecture 6: Products |
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Lecture 7: Compactness |
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Lecture 8: Compactness in metric spaces |
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Lecture 9: Metric compactness continued |
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Lecture 10: Compactness and normed spaces |
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Lecture 12: Topological spaces |
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Lecture 13: Continuous functions and subspaces |
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Lecture 14: Bases and subbases |
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Lecture 15: Products and quotients |
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Lecture 16: Separation axioms |
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Lecture 17: $T_3$ and $T_4$ |
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Lecture 18: Uryshon and Tietze |
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Lecture 19: Compactness |
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Lecture 20: Connectedness |
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Lecture 21: Locally compact spaces and infinite products |
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Lecture 23: Groups and homotopies |
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Lecture 24: Paths and the fundamental group |
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Lecture 25: Induced homomorphisms and base points |
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Lecture 26: Covering spaces |
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Lecture 27: Path lifting |
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Lecture 28: Covers and $\pi_1$ |
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Lecture 29: Classification |
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