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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 2024
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:3/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English
Teaching methods:	full-time

Guarantor:	doc. Mgr. Benjamin Vejnar, Ph.D.
Teacher(s):	doc. Mgr. Benjamin Vejnar, Ph.D.
Class:	M Mgr. MA M Mgr. MA > Volitelné
Classification:	Mathematics > Topology and Category
Incompatibility :	NMAT042
Interchangeability :	NMAT042

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

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.

Last update: T_KMA (25.04.2013)

Course completion requirements -

The exam is oral and its content is captured in the sylabus.

"Zapocet" is given to anyone who passes the exam.

Last update: Spurný Jiří, prof. RNDr., Ph.D., DSc. (12.01.2024)

Literature -

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

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

Syllabus -

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.

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

Entry requirements -

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

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