Difference between revisions of "Math 553: Foundations of Topology 1"
From MathWiki
m (moved Math 553 to Math 553: Foundations of Topology 1) 

(No difference)

Revision as of 15:41, 3 April 2013
Contents
Catalog Information
Title
Foundations of Topology 1.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
F
Prerequisite
Mth 451 or instructor's consent
Description
Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, and complete metric spaces.
Desired Learning Outcomes
Students should gain a familiarity with the general topology that is used throughout mathematics.
Minimal learning outcomes
 Set Theory
 Finite, countable, and uncountable sets
 Wellordered sets
 Topological Spaces
 Basis for a topology
 Product topology
 Metric topology
 Continuous Functions
 Connectedness
 Compactness
 Tychonoff Theorem
 Countability and Separation Axioms
 Countable basis
 Countable dense subsets
 Normal spaces
 Urysohn Lemma
 Tietze Extension Theorem
 Metrization
 Urysohn Metrization Theorem
 Complete Metric Spaces
Textbooks
Possible textbooks for this course include (but are not limited to):
Additional topics
Paracompactness, the NagataSmirnov Metrization Theorem, Ascoli's Theorem, Baire Spaces and dimension theory as time allows.
Courses for which this course is prerequisite
Math 554