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