MATH 553
Foundations of Topology 1
Mathematics
College of Physical and Mathematical Sciences
Course Description
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.
When Taught
Fall
Grade Rule
Grade Rule 8: A, B, C, D, E, I (Standard grade rule)
Min
3
Fixed
3
Fixed
3
Fixed
0
Other Prerequisites
Math 341 or equivalent.
Title
Overview
Learning Outcome
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
Title
Learning Outcomes
Learning Outcome
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.
