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Course, academic year 2024/2025
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Topological and Geometric Properties of Convex Sets 1 - NMMA575
Title: Topologické a geometrické vlastnosti konvexních množin 1
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2024
Semester: winter
E-Credits: 3
Hours per week, examination: winter 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, English
Teaching methods: full-time
Guarantor: prof. RNDr. Jiří Spurný, Ph.D., DSc.
Teacher(s): prof. RNDr. Jiří Spurný, Ph.D., DSc.
Class: M Mgr. MA
M Mgr. MA > Volitelné
Classification: Mathematics > Geometry, Topology and Category
Incompatibility : NRFA073
Annotation -
The lecture is devoted to studying properties of compact convex sets in locally convex spaces.
Last update: T_KMA (26.04.2013)
Aim of the course - Czech

Přednáška je věnována základním i hlubším vlastnostem kompaktních konvexních množin a jejich aplikacím.

Last update: Spurný Jiří, prof. RNDr., Ph.D., DSc. (23.09.2022)
Course completion requirements - Czech

Zkouška je ústní, přičemž zkoušena bude odpřednesená látka.

Last update: Spurný Jiří, prof. RNDr., Ph.D., DSc. (23.09.2022)
Literature - Czech

Alfsen: Compact convex sets and boundary integrals

Asimow, Ellis: Convexity theory and its applications in functional analysis

Johnson, Lindenstrauss: Handbook of geometry of Banach spaces I, II

Last update: Spurný Jiří, prof. RNDr., Ph.D., DSc. (23.09.2022)
Syllabus -

Basics of the Choquet theory, integral representation theorems, simplices, topological properties of extreme points, Poulsen's simplex, Lazar's selection theorem.

Last update: T_KMA (26.04.2013)
Entry requirements -

Basic courses of functional analysis and topology

Last update: T_KMA (26.04.2013)
 
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