Math 553: Foundations of Topology 1
Foundations of Topology 1.
(Credit Hours:Lecture Hours:Lab Hours)
Math 451 or instructor's consent.
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
- Tychonoff Theorem
- Countability and Separation Axioms
- Countable basis
- Countable dense subsets
- Normal spaces
- Urysohn Lemma
- Tietze Extension Theorem
- Urysohn Metrization Theorem
- Complete Metric Spaces
Possible textbooks for this course include (but are not limited to):
Paracompactness, the Nagata-Smirnov Metrization Theorem, Ascoli's Theorem, Baire Spaces and dimension theory as time allows.
Courses for which this course is prerequisite