MU:MU24022 Topology - Course Information

MU24022 Topology

Extent and Intensity

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

Teacher(s)

doc. RNDr. Jana Kopfová, Ph.D. (lecturer)
doc. RNDr. Hynek Baran, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Jana Kopfová, Ph.D.
Mathematical Institute in Opava

Timetable

Wed 8:55–10:30 108

• Timetable of Seminar Groups:

MU24022/01: Tue 11:25–13:00 205, H. Baran

Prerequisites (in Czech)

TYP_STUDIA(N)

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

• Applied Mathematics (programme MU, N1101)

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)

Study Materials
The course can also be completed outside the examination period.

Teacher's information

The examination is written and oral.

• Enrolment Statistics (recent)
  
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