SUBJECT
Title
Introduction to topology
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
2
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Topological spaces and continuous maps. Constructions of spaces: subspaces, quotient spaces, product spaces, functional spaces. Separation axioms, Urison’s lemma. Tietze theorem.Countability axioms., Urison’s metrization theorem. Compactness, compactifications, compact metric spaces. Connectivity, path-connectivity. Fundamental group, covering maps.
The fundamental theorem of Algebra, The hairy ball theorem, Borsuk-Ulam theorem.
Readings
J. L. Kelley: General Topology, 1957, Princeton.