#
MU:MU02020 Introduction to Topology - Course Information

## MU02020 Introduction to Topology

**Mathematical Institute in Opava**

Summer 2021

**Extent and Intensity**- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- doc. RNDr. Zdeněk Kočan, Ph.D. (lecturer)

Mgr. Jakub Vašíček (seminar tutor) **Guaranteed by**- RNDr. Jana Hantáková, Ph.D.

Mathematical Institute in Opava **Timetable**- Mon 8:55–10:30 R1
- Timetable of Seminar Groups:

*J. Vašíček* **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**- Mathematical Methods and Modelling (programme MU, Bc-M)
- General Mathematics (programme MU, Bc-M)

**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)

- 1. Topological spaces (topology, basis, open and closed sets, interior, exterior and boundary of a set, limit points and closure, dense set)
**Literature****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.

- Enrolment Statistics (recent)

- Permalink: https://is.slu.cz/course/sumu/summer2021/MU02020