MAT5243
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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 

12  Review of set theory and metric spaces  12  Cardinal and ordinal arithmetic, metric and pseudometric spaces, metric topologies.  Real Analysis, undergraduate topology. 
3  Topological spaces  35 
 
45  New spaces from old  69 
 
67  Convergence  1012 
 
57  Separation and countability  1316 
 
89  Compactness  1719 
 
10end  Metrization  3538 
