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Week - 1 |
Compactness of topological spaces, Compact spaces and compactness of subspaces |
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Week - 2 |
Compactness of topological spaces; Some relations among compactness, closed sets and continuous functions |
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Week - 3 |
Compactness of topological spaces; Compactness of product spaces, some examples |
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Week - 4 |
Compactness of topological spaces; Countably compact and sequentially compact spaces |
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Week - 5 |
Compactness of topological spaces; Locally compact spaces, compactness and completeness in metric spaces |
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Week - 6 |
Connectedness; Connected spaces and connected subsets |
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Week - 7 |
Connectedness; connectedness and continuous functions, connectedness of product spaces |
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Week - 8 |
Connectedness; Path-connected spaces, components, locally connected spaces |
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Week - 9 |
Connectedness; Disconnected and totally disconnected spaces |
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Week - 10 |
Complete Metric Spaces: Completeness concept |
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Week - 11 |
Complete Metric Spaces: Fixed point theorems |
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Week - 12 |
Complete Metric Spaces: Contraction theorems |
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Week - 13 |
Arzela-Ascoli theorems |
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Week - 14 |
Completion of metric spaces |
Eskisehir Technical University Info Package