Difference between revisions of "MAT5243"
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|| Separation and countability axioms, regularity and complete regularity | || Separation and countability axioms, regularity and complete regularity | ||
|- | |- | ||
| − | | 8- | + | | 8-9 |
|| [[Compactness]] | || [[Compactness]] | ||
|| 10-12 | || 10-12 | ||
|| Characterizations of compactness, connections between compactness and continuity | || Characterizations of compactness, connections between compactness and continuity | ||
|- | |- | ||
| − | | | + | | 10-end |
|| [[Metrization]] | || [[Metrization]] | ||
|| metrizable spaces | || metrizable spaces | ||
|| Search trees, spanning trees, the Traveling Salesman Problem | || Search trees, spanning trees, the Traveling Salesman Problem | ||
|} | |} | ||
Revision as of 11:57, 23 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 | |
| 8-9 | Compactness | 10-12 | Characterizations of compactness, connections between compactness and continuity | |
| 10-end | Metrization | metrizable spaces | Search trees, spanning trees, the Traveling Salesman Problem |
