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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 2016 to 2016
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:	doc. Mgr. Benjamin Vejnar, Ph.D.
Class:	M Mgr. MA M Mgr. MA > Volitelné
Classification:	Mathematics > Topology and Category
Incompatibility :	NMAT042
Interchangeability :	NMAT042

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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.

Literature - Czech

Last update: T_KMA (25.04.2013)

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,

metrization theorems: Urysohn, Bing-Nagata-Smirnov, Bing.

3: Connectedness and local conectedness: components, quasi-components,

continua, decomposability and indecomposability.

4.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, compact metric case, Katetov-Morita theorem, dimension

of R^n.