COURSE NUMBER AND TITLE: MATH 4520 General Topology

CREDIT HOURS: 3

CATALOG DESCRIPTION: A study of general topology including applications to Euclidean spaces, surfaces, topological invariants, continuous functions and homeomorphisms.

PREREQUISITE(S): MATH 2013 or permission of instructor.

SUGGESTED TEXT(S):
A First Course in Topology by Robert A. Conover
Topology of Surfaces by L. Christine Kinsey

COURSE OUTLINE:

1. Elementary Set Theory
   • Sets and Notation
   • Operations on sets
   • Functions and Composition of Functions
   • Inverse functions and bijections
2. Topological Spaces
   • Definition of a topological space
   • Examples: R, R2, etc.
   • Closed sets; closure of a set
   • Basis and sub-basis of a topology; Generated topologies
3. Mappings on topological spaces
   • Continuous mappings
   • Homeomorphisms
4. Connectivity
   • Definition
   • Components and local connectivity
   • Path connectivity
5. Compactness
   • Definition
   • Equivalences of compactness on the real number line
   • Consequences of compactness
6. Additional topics may include:
   • Product spaces and the product topology
   • Quotient spaces and the quotient topology
   • Metric spaces and the metric topology
   • Separation axioms and Hausdorff spaces
   • Toplogical invariants