Mathematics
 

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.
MATH
553
 Hours3.0 Credit, 3.0 Lecture, 0.0 Lab
 PrerequisitesMath 341 or equivalent.
 TaughtFall
 ProgramsContaining 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

  1. Set Theory
  2. Topological Spaces
  3. Continuous Functions
  4. Connectedness
  5. Compactness
  6. Tychonoff Theorem
  7. Countability and Separation Axioms
  8. Countable basis
  9. Countable dense subsets
  10. Normal spaces
  11. Urysohn Lemma
  12. Tietze Extension Theorem
  13. Metrization
  14. Complete Metric Spaces