MAT5243

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	Uniform spaces, metrizable uniform spaces.