Introduction to Topology (TOP1)

Instructor: Agnes Szilard, PhD
Text: Notes will be distributed in class.
Reference book: Munkres: Topology, Prentice Hall, 2000

Prerequisites: Calculus, basics of set theory and group theory.
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 use it to study covering spaces. Time permitting we will also look at the classification of compact surfaces.
Throughout the course we will study numerous examples and applications.