PřF:M6140 Topology - Course Information

M6140 Topology

Faculty of Science
Spring 2000

Extent and Intensity

2/1/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Jiří Rosický, DrSc. (lecturer)

Guaranteed by

Prerequisites (in Czech)

M3100 Mathematical Analysis III

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

Syllabus

Topological spaces: topological spaces, closed sets, closure
Continuous maps: continuous maps, homeomorphisms
Subspaces and products: subspaces, products
Separation axioms: T0 and T1 spaces, Hausdorff spaces, regular spaces, normal spaces
Compact spaces: compact spaces, Tichonov theorem
Connected spaces: connected spaces, components, pathwise connected spaces, locally connected spaces, continuum, Cantor discontinuum
Homotopy: homotopy, simply connected spaces, fundamental group, applications of a fundamental group
Real functions: completely regular spaces, Urysohn lemma, Tietze theorem
Locally compact spaces: locally compact spaces, one-point compactification
Brouwer fix point theorem: complexes, triangulation, Sperner lemma, Brouwer theorem

Literature

PULTR, Aleš. Podprostory euklidovských prostorů. Vyd. 1. Praha: SNTL - Státní nakladatelství technické literatury, 1986, 253 s. info
CHVALINA, Jan. Obecná topologie. Vyd. 1. Brno: Univerzita J.E. Purkyně, 1984, 193 s. info
PULTR, Aleš. Úvod do topologie a geometrie. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1982, 231 s. info

Language of instruction

Czech

Further Comments

The course is taught annually.
The course is taught: every week.