### 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.''