Foundations of Topology 1
Foundations of Topology 1
An introduction to the topology of the plane and algebraic topology: simplicial complexes, CW-complexes, the fundamental group, classification of covering spaces, homotopy, Seifer-van Kampen Theorem, Jordan Curve Theorem, and Invariance of Domain.
| Hours | 3.0 Credit, 3.0 Lecture, 0.0 Lab |
| Prerequisites | Math 341 or equivalent. |
| Taught | Fall |
| Programs | Containing MATH 553 |
Course Outcomes:
Learning Outcomes
Students should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor. For more detailed information visit the Math 553 Wiki page.
Overview
- Set Theory
- Topological Spaces
- Continuous Functions
- Connectedness
- Compactness
- Tychonoff Theorem
- Countability and Separation Axioms
- Countable basis
- Countable dense subsets
- Normal spaces
- Urysohn Lemma
- Tietze Extension Theorem
- Metrization
- Complete Metric Spaces