Difference between revisions of "MAT5243"

Revision as of 20:57, 18 March 2023

Introduction to the general theory of topological spaces

Sample textbook:

[1] Stephen Willard, General Topology, Dover, 20.04

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.	MAT1313, CS2233/2231, or instructor consent.
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
8-10	Compactness	10-12	Characterizations of compactness, connections between compactness and continuity
9-10	Metrization	metrizable spaces	Search trees, spanning trees, the Traveling Salesman Problem

@@ Line 1: / Line 1: @@
-Review of metric spacxes, general topological spaces, continuous functions, the product topology, filters and nets, compactness, connected spaces.
+Introduction to the general theory of topological spaces
+'''Sample textbook''':
+[1] Stephen Willard, ''General Topology'', Dover, 20.04
+==Topics List==
+{| class="wikitable sortable"
+! 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.
+|| MAT1313, CS2233/2231, or instructor consent.
+|-
+|  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
+|-
+|  8-10
+|| [[Compactness]]
+|| 10-12
+|| Characterizations of compactness, connections between compactness and continuity
+|-
+|  9-10
+|| [[Metrization]]
+|| metrizable spaces
+|| Search trees, spanning trees, the Traveling Salesman Problem
+|}