General Topology

Department: 
MATH
Course Number: 
6451
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
no regular schedule

Introduction to topological and metric spaces. Continuity, compactness, convergence, completion. Product and quotient spaces. Elementary homotopy.

Prerequisites: 

MATH 4317 or MATH 4431

Course Text: 

No text

Topic Outline: 
  • Pseudometric spaces
  • Topological spaces
  • Continuity and the weak topology
  • Connectivity
  • Compactness
  • Product spaces and the Tychonoff Theorem
  • Convergence-sequences, nets, and filters
  • Uniform spaces and completeness
  • Euclidean spaces
  • Quotient spaces, hyperspaces, and multifunctions
  • Homotopy and the fundamental group