Difference between revisions of "MAT5243"
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|| 1-2 | || 1-2 | ||
|| Cardinal and ordinal arithmetic, metric and pseudometric spaces, metric topologies. | || Cardinal and ordinal arithmetic, metric and pseudometric spaces, metric topologies. | ||
| − | || | + | || Real Analysis, undergraduate topology. |
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| 3-4 | | 3-4 | ||
Revision as of 20:58, 18 March 2023
Introduction to the general theory of topological spaces
Sample textbook:
[1] Stephen Willard, General Topology, Dover, 20.04
Topics List
| Week | Topic | Sections from Tucker's book | Subtopics | Prerequisite |
|---|---|---|---|---|
| 1-2 | Review of set theory and metric spaces | 1-2 | Cardinal and ordinal arithmetic, metric and pseudometric spaces, metric topologies. | Real Analysis, undergraduate topology. |
| 3-4 | Product spaces | 3-5 | Products and quotient topologies | |
| 5-7 | Separation and countability | 6-9 | Separation and countability axioms, regularity and complete regularity | |
| 8-10 | Compactness | 10-12 | Characterizations of compactness, connections between compactness and continuity | |
| 9-10 | Metrization | metrizable spaces | Search trees, spanning trees, the Traveling Salesman Problem |
