MU:MU02020 Introduction to Topology - Course Information

MU02020 Introduction to Topology

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

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

Timetable

Mon 8:55–10:30 R1

• Timetable of Seminar Groups:

MU02020/01: Wed 15:35–17:10 203, 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)
  

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.

• Enrolment Statistics (Summer 2021, recent)
  
• Permalink: https://is.slu.cz/course/sumu/summer2021/MU02020