MU24022 Topology

Mathematical Institute in Opava
Winter 2017
Extent and Intensity
2/2/0. 2 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michaela Mlíchová, Ph.D. (lecturer)
doc. RNDr. Jana Hantáková, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Michaela Mlíchová, Ph.D.
Mathematical Institute in Opava
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
Course objectives
The course will provide the students with the basic knowledge of general topology.
Syllabus
  • 1. Topological spaces - topology, open and closed sets, Euclidean topology, basis, interior and exterior, limit points and closure, neighbourhoods, connectedness, subspaces.
    2. Homeomorphisms and continuous mappings.
    3. Metric spaces - metric, convergence of sequences.
    4. Compactness - compact spaces, Heine-Borel theorem.
    5. Finite products - product topology, Tychonoff's theorem for finite products, products and connectedness.
    6. Countable products - product topology.
    7. Tychonoff's theorem - product topology for all products, Tychonoff's theorem.
    8. Quotient spaces.
Literature
    required literature
  • S. A. Morris. Topology without tears. 2016. URL info
    recommended literature
  • D. Krupka, O. Krupková. Topologie a geometrie, 1. Obecná topologie. SPN, Praha, 1989. info
  • J. R. Munkres. Topology, A First Course. Prentice Hall, New Jersey, 1975. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The examination is written and oral.
The course is also listed under the following terms Winter 2014, Winter 2015, Winter 2016, Winter 2018, Winter 2019, Winter 2020.
  • Enrolment Statistics (Winter 2017, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2017/MU24022