Introduction to Topology — TOP

Instructor:  Ágnes SZILARD PhD

Text:  Your class notes and online notes (will be available on the class homepage).

Prerequisites:  Solid knowledge of calculus (like limits and continuity, manipulating with sets and fuctions) is indispensable. Rudiments of group theory (not much more than uderstanding what the words group, subgroup, homomorphism, isomorphism mean) will also be necessary in the second half of the course.

Course description:  This is a standard introductory course the goal of which is to get acquainted with the basic notions of the field. Thus we start with point-set topology and a thorough discussion of metric and topological spaces, continuity, connectedness, compactness. We then get a glimpse of algebraic topology - the notion of the fundamental group of a topological space will be introduced and we will study covering spaces. The machinery developed will allow us to look at one of the major theorems of topology: the classification of compact, connected surfaces. Throughout the course we will study numerous examples and applications.