MU02020 Introduction to Topology

Mathematical Institute in Opava
Summer 2024
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jana Hantáková, Ph.D. (lecturer)
RNDr. Adam Hlaváč, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jana Hantáková, Ph.D.
Mathematical Institute in Opava
Timetable
Wed 8:05–9:40 R1
  • Timetable of Seminar Groups:
MU02020/01: Wed 13:55–15:30 R2, A. Hlaváč
Prerequisites (in Czech)
TYP_STUDIA(B)
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, basis, open and closed sets, interior, exterior and boundary of a set, limit points and closure, dense set)
    2. Euclidean topology (definition and basic properties)
    3. Continuous mappings, homeomorphisms (examples, topological invariants)
    4. Metric spaces (distance function, equivalent metric spaces, sequences in metric spaces, complete metric space)
    5. Compactness and connectedness (Heine-Borel theorem, Tychonoff theorem)
    6. Topological constructions (product topology, subspace topology, quotient topology)
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)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
Course credit prior to examination is granted for written tests (3 written tests during the semester, 50% is needed to pass). The examination is both written and oral.
The course is also listed under the following terms Summer 2021, Summer 2022, Summer 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2024/MU02020