401-2554-00L  Topology

SemesterSpring Semester 2020
LecturersA. Carlotto
Periodicityyearly recurring course
Language of instructionEnglish

AbstractTopics covered include: Topological and metric spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces.
ObjectiveAn introduction to topology i.e. the domain of mathematics that studies how to define the notion of continuity on a mathematical structure, and how to use it to study and classify these structures.
LiteratureWe will follow these, freely available, standard references by Allen Hatcher:

i) Link

(for the part on General Topology)

ii) Link

(for the part on basic Algebraic Topology).

Additional references include:

"Topology" by James Munkres (Pearson Modern Classics for Advanced Mathematics Series)

"Counterexamples in Topology" by Lynn Arthur Steen, J. Arthur Seebach Jr. (Springer)

"Algebraic Topology" by Edwin Spanier (Springer).
Prerequisites / NoticeThe content of the first-year courses in the Bachelor program in Mathematics. In particular, each student is expected to be familiar with notion of continuity for functions from/to Euclidean spaces, and with the content of the corresponding basic theorems (Bolzano, Weierstrass etc..). In addition, some degree of scientific maturity in writing rigorous proofs (and following them when presented in class) is absolutely essential.