MAT 530 (Fall 1995) Topology/Geometry I


Syllabus

The Official MAT 530 Syllabus

Basic point set topology:
Metric spaces
Topological spaces and continuous maps
Comparison of topologies
Separation axioms and limits
Countability axioms
Compactness and paracompactness
Connectedness
Product spaces
Function spaces and their topologies

Introduction to algebraic topology:
Fundamental group and covering spaces
Finite simplicial complexes
Simplicial homology with integer coefficients
Short discussion of other coefficients, especially Z_2 and R
Idea of cohomology
Applications

... and unofficially

``no one ever goes past covering spaces.''