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Fundamentals of Theory of Metric Spaces - NMMA262

Title:	Základy teorie metrických prostorů
Guaranteed by:	Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2013 to 2014
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Petr Simon, DrSc.
Class:	M Bc. OM M Bc. OM > Doporučené volitelné M Bc. OM > 2. ročník
Classification:	Mathematics > Real and Complex Analysis
Incompatibility :	NMAI020
Interchangeability :	NMAI020

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: G_M (15.05.2013)

Non-obligatory course for the first year of study. Metric spaces, continuous and uniformly continuous mappigs, topology of metric space. Totally bounded metric spaces, complete metric spaces, completion, Lavrent'ev theorem, Baire theorem. Compact metric spaces, discontinuum. Connected metric spaces and metric continua.

Aim of the course - Czech

Last update: G_M (15.05.2013)

Naučit základy teorie metrických prostorů

Literature - Czech

Last update: G_M (15.05.2013)

E. Čech, Bodové množiny, Academia, Praha 1966

Syllabus -

Last update: G_M (15.05.2013)

1. Metric spaces, continuous and uniformly continuous mappings,

open and closed sets, interion, closure, topologically equivalent metrics.

Subspace, sum and product of metric spaces.

2. Totally bounded metric spaces.

3. Complete metric spaces, completion, Lavrent'ev theorem, Baire theorem

Kuratowski theorem.

4. Compact metric spaces, discontinuum, Alexandroff theorem.

5. Connected metric spaces and metric continua, their basic properties.