MAT5243

From Department of Mathematics at UTSA
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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
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
  • Uniform spaces
  • Metrization of uniform spaces.