MAT5243

From Department of Mathematics at UTSA
Jump to navigation Jump to search

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