Elementary Topology

MATH 32101

3

MATH 26100


Spring


Introduction to topology, including metric spaces, abstract topological spaces, continuous functions, connectedness, compactness, curves, Cantor sets, coninua, and the Baire Category Theorem.  Also, an introduction to surfaces, including spheres, tori, the Mobius band, the Klein bottle and a description of their classification.

The course will begin with a study of metric spaces then move to abstract topological spaces and continuous functions. Then a variety of topological properties and how they relate to specified examples will be examined. Topological ideas provide an excellent background for courses such as differential geometry, real analysis and complex analysis.