Introduction to Topology (TOP1)

Instructor: Dr. Ágnes Szilard (TOPA), Dr. Árpád Tóth (TOPB)

Text: Class notes, and notes 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 study covering spaces. The machinery developed will allow us to look at one of the major theorems of topology: the classification of compact surfaces.
Throughout the course we will study numerous examples and applications.