Introduction to Topology (TOP1)
Instructor: Dr. Ágnes Szilard (TOPA), Dr. Árpád Tóth (TOPB)
Text: Class notes, and notes distributed in class.
Munkres: Topology, Prentice Hall, 2000
Prerequisites: Calculus, basics of set theory and group
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.