MAT 530 (Fall 1995) Topology/Geometry I


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
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

... and unofficially

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