Subjects(version: 944)
General Topology 2 - NMMA462
Title: Obecná topologie 2 Department of Mathematical Analysis (32-KMA) Faculty of Mathematics and Physics from 2023 summer 6 summer s.:2/2, C+Ex [HT] unlimited unlimited no no taught Czech, English full-time full-time
Guarantor: prof. RNDr. Jiří Spurný, Ph.D., DSc. M Mgr. MAM Mgr. MA > Volitelné Mathematics > Topology and Category NMAT042 NMAT042
 Annotation - ---CzechEnglish
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 - ---CzechEnglish
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 - ---CzechEnglish
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 - ---CzechEnglish
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 - ---CzechEnglish
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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