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 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	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	Separation and countability	13-16	Separation axioma Countability axioms
8-9	Compactness	17-19	Characterizations of compactness Connections between compactness and continuity
10-end	Metrization	35-38 metrizable spaces	Uniform spaces Metrization of uniform spaces.