Difference between revisions of "MAT5243"

Latest revision as of 21:56, 25 March 2023

Introduction to the general theory of topological spaces

Sample textbook:

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

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.

@@ 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 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.
+|}