Difference between revisions of "Math 553: Foundations of Topology 1"
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Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, and complete metric spaces. | Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, and complete metric spaces. |
Revision as of 15:57, 23 March 2011
Contents
Catalog Information
Title
Foundations of Topology 1.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
F
Prerequisite
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
- Well-ordered 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 Nagata-Smirnov Metrization Theorem, Ascoli's Theorem, Baire Spaces and dimension theory as time allows.
Courses for which this course is prerequisite
Math 554