Difference between revisions of "Math 553: Foundations of Topology 1"
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=== Prerequisite === | === Prerequisite === | ||
[[Math 451]] or instructor's consent. | [[Math 451]] or instructor's consent. | ||
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=== Description === | === Description === | ||
Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, complete metric spaces, function spaces, and Baire spaces. | Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, complete metric spaces, function spaces, and Baire spaces. | ||
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== Desired Learning Outcomes == | == Desired Learning Outcomes == | ||
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Students should gain a familiarity with the general topology that is used throughout mathematics. | Students should gain a familiarity with the general topology that is used throughout mathematics. | ||
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=== Minimal learning outcomes === | === Minimal learning outcomes === | ||
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<div style="-moz-column-count:2; column-count:2;"> | <div style="-moz-column-count:2; column-count:2;"> | ||
# Set Theory | # Set Theory | ||
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#* Urysohn Metrization Theorem | #* Urysohn Metrization Theorem | ||
# Complete Metric Spaces | # Complete Metric Spaces | ||
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</div> | </div> | ||
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=== Additional topics === | === Additional topics === | ||
Paracompactness, the Nagata-Smirnov Metrization Theorem, Ascoli's Theorem, Baire Spaces and dimension theory as time allows. | Paracompactness, the Nagata-Smirnov Metrization Theorem, Ascoli's Theorem, Baire Spaces and dimension theory as time allows. | ||
Revision as of 13:48, 26 May 2010
Contents
Catalog Information
Title
Foundations of Topology 1.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
F
Prerequisite
Math 451 or instructor's consent.
Description
Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, complete metric spaces, function spaces, and Baire 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
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
