Difference between revisions of "MAT5243"
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==Topics List== | ==Topics List== | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
| − | ! Week !! Topic !! Sections from | + | ! Week !! Topic !! Sections from Willard's book !! Subtopics !! Prerequisite |
|- | |- | ||
| 1-2 | | 1-2 | ||
| Line 17: | Line 17: | ||
|| Real Analysis, undergraduate topology. | || Real Analysis, undergraduate topology. | ||
|- | |- | ||
| − | | 3 | + | | 3 |
| − | || [[ | + | || [[Topological spaces]] |
|| 3-5 | || 3-5 | ||
| − | || | + | || |
| + | * Neighborhoods | ||
| + | * Bases | ||
| + | * Subbases | ||
| + | |- | ||
| + | | 4-5 | ||
| + | || [[New spaces from old]] | ||
| + | || 6-9 | ||
| + | || | ||
| + | * Subspaces | ||
| + | * Continuous functions | ||
| + | * Product topologies | ||
| + | * Quotient topologies | ||
| + | |- | ||
| + | | 6-7 | ||
| + | || [[Convergence]] | ||
| + | || 10-12 | ||
| + | || | ||
| + | * Filters and ultrafilter limits | ||
| + | * Characterization of topologies and continuity through convergence | ||
|- | |- | ||
| 5-7 | | 5-7 | ||
|| [[Separation and countability]] | || [[Separation and countability]] | ||
| − | || | + | || 13-16 |
| − | || Separation | + | || |
| + | * Separation axioma | ||
| + | * Countability axioms | ||
| + | |||
|- | |- | ||
| − | | 8- | + | | 8-9 |
|| [[Compactness]] | || [[Compactness]] | ||
| − | || | + | || 17-19 |
| − | || Characterizations of compactness | + | || |
| + | * Characterizations of compactness | ||
| + | * Connections between compactness and continuity | ||
|- | |- | ||
| − | | | + | | 10-end |
|| [[Metrization]] | || [[Metrization]] | ||
| − | || | + | || 35-38 |
| − | || | + | || |
| + | * Uniform spaces | ||
| + | * Metrization of uniform spaces. | ||
|} | |} | ||
Latest revision as of 21:56, 25 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 Willard'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 | Topological spaces | 3-5 |
| |
| 4-5 | New spaces from old | 6-9 |
| |
| 6-7 | Convergence | 10-12 |
| |
| 5-7 | Separation and countability | 13-16 |
| |
| 8-9 | Compactness | 17-19 |
| |
| 10-end | Metrization | 35-38 |
|
