MAT5243 - Revision history

Jose.iovino at 21:22, 17 August 2025

2025-08-17T21:22:19Z

Jose.iovino: /* Topics List */

2023-03-26T03:56:55Z

Topics List

Jose.iovino: /* Topics List */

2023-03-26T03:56:29Z

Topics List

Jose.iovino: /* Topics List */

2023-03-26T03:55:29Z

Topics List

Jose.iovino: /* Topics List */

2023-03-26T03:54:40Z

Topics List

Jose.iovino at 12:04, 25 March 2023

2023-03-25T12:04:14Z

Jose.iovino: /* Topics List */

2023-03-23T17:57:04Z

Topics List

Jose.iovino: /* Topics List */

2023-03-19T02:58:21Z

Topics List

Jose.iovino at 02:57, 19 March 2023

2023-03-19T02:57:43Z

Jose.iovino: Created page with "Review of metric spacxes, general topological spaces, continuous functions, the product topology, filters and nets, compactness, connected spaces."

2023-03-09T21:36:01Z

Created page with "Review of metric spacxes, general topological spaces, continuous functions, the product topology, filters and nets, compactness, connected spaces."

New page

Review of metric spacxes, general topological spaces, continuous functions, the product topology, filters and nets, compactness, connected spaces.

@@ Line 3: / Line 3: @@
 '''Sample textbook''':
-[1] Stephen Willard, ''General Topology'', Dover, 20.04
+[1] Stephen Willard, ''General Topology'', Dover, 2004
@@ Line 45: / Line 45: @@
 || 13-16
 ||
-* Separation axioma
+* Separation axioms
 * Countability axioms

@@ Line 59: / Line 59: @@
 || [[Metrization]]
 || 35-38
 ||
 * Uniform spaces
 * Metrization of uniform spaces.
 |}

@@ Line 24: / Line 24: @@
 * Bases
 * Subbases
-|  4-5
+|-
-|-
+|  4-5
 || [[New spaces from old]]
 || 6-9

@@ Line 24: / Line 24: @@
 * Bases
 * Subbases
 |  4-5
 || [[New spaces from old]]
 || 6-9

@@ Line 9: / Line 9: @@
 ==Topics List==
 {| class="wikitable sortable"
-! Week !! Topic !! Sections from Tucker's book !! Subtopics !! Prerequisite
+! Week !! Topic !! Sections from Willard's book !! Subtopics !! Prerequisite
 |-
 |  1-2
@@ Line 17: / Line 17: @@
 || Real Analysis, undergraduate topology.
 |-
-|  3-4
+|  3
-|| [[Product spaces]]
+|| [[Topological spaces]]
 || 3-5
-|| Products and quotient topologies
+||
 |-
 |  5-7
 || [[Separation and countability]]
-|| 6-9
+|| 13-16
-|| Separation and countability axioms, regularity and complete regularity
+||
 |-
 |  8-9
 || [[Compactness]]
-|| 10-12
+|| 17-19
-|| Characterizations of compactness, connections between compactness and continuity
+||
 |-
 |  10-end
 || [[Metrization]]
-|| metrizable spaces
+|| 35-38
-|| Uniform spaces, metrizable uniform spaces.
+* metrizable spaces
 |}

@@ Line 15: / Line 15: @@
 || 1-2
 || Cardinal and ordinal arithmetic, metric and pseudometric spaces, metric topologies.
-|| MAT1313, CS2233/2231, or instructor consent.
+|| Real Analysis, undergraduate topology.
 |-
 |  3-4

← Older revision		Revision as of 02:57, 19 March 2023
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
		+	\|}