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Course, academic year 2023/2024
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General Topology 2 - NMMA462
Title: Obecná topologie 2
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Jiří Spurný, Ph.D., DSc.
Class: M Mgr. MA
M Mgr. MA > Volitelné
Classification: Mathematics > Topology and Category
Incompatibility : NMAT042
Interchangeability : NMAT042
Annotation -
Last update: T_KMA (25.04.2013)
Continuation of the course General Topology 1. It is also necessary for the study branch Mathematical Structures. It provides an information about more advaced parts of the discipline.
Course completion requirements -
Last update: doc. Mgr. Benjamin Vejnar, Ph.D. (23.04.2020)

You need to have "zapocet" to take the exam. The exam is oral and its content is captured in the sylabus.

"Zapocet" is given for active participation on the seminar.

Literature -
Last update: doc. Mgr. Benjamin Vejnar, Ph.D. (29.10.2019)

R. Engelking, General Topology, PWN Warszawa 1977

J. L. Kelley, General Topology, D. Van Nostrand, New York 1957 (ruský překlad Obščaja Topologija, Nauka, Moskva 1968)

E. Čech, Topological Spaces, Academia, Praha 1966

Syllabus -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (08.12.2017)

1. Cech-complete spaces: Definition, Frolik's characterization,

Baire theorem.

2. Paracompact spaces: Stone theorem, equivalent descriptions, fine uniformity.

3. Metrization theorems: Urysohn, Bing-Nagata-Smirnov, Bing.

4. Connectedness and local conectedness: components, quasi-components,

basic theory of continua.

5. Topological groups: Quotient groups, connected groups.

5. Disconnectedness: Totally disconnected spaces, zero-dimensional spaces,

strongly zero-dimensional spaces.

6. Dimension theory: Dimensions dim, ind, Ind, basic inequalities,

sum theorem for dim, dimension of metric case and of R^n.

Entry requirements -
Last update: doc. Mgr. Benjamin Vejnar, Ph.D. (29.10.2019)

The knowledge of the theory of topological spaces in the range of the lecture Topology 1.

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