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Properties of Poulsen simplices
Jaroň, Zdeněk ; Spurný, Jiří (advisor) ; Kurka, Ondřej (referee)
Title: Properties of Poulsen simplices Author: Zdeněk Jaroň Department: Department of Mathematical Analysis Supervisor: Doc. RNDr. Jiří Spurný, Ph.D. Abstract: In the present thesis, we study a generalisation of concept of the Poulsen simplex in general, non-metrizable case. First, for any given simplex F we con- struct a new one S, containing F as a face, having dense set of extreme points and preserving some important properties of F. In the next part, we employ this con- struction to build up, for any given infinite cardinal κ, two simplices S1, S2 with dense extreme boundary, with density character equal to κ and with spaces of affine functions Ac (S1) and Ac (S2) having the same density character, but which are not affinely homeomorphic. Keywords: Poulsen simplex, projective limit, Helly space
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Properties of Poulsen simplices
Jaroň, Zdeněk ; Spurný, Jiří (advisor) ; Kurka, Ondřej (referee)
Title: Properties of Poulsen simplices Author: Zdeněk Jaroň Department: Department of Mathematical Analysis Supervisor: Doc. RNDr. Jiří Spurný, Ph.D. Abstract: In the present thesis, we study a generalisation of concept of the Poulsen simplex in general, non-metrizable case. First, for any given simplex F we con- struct a new one S, containing F as a face, having dense set of extreme points and preserving some important properties of F. In the next part, we employ this con- struction to build up, for any given infinite cardinal κ, two simplices S1, S2 with dense extreme boundary, with density character equal to κ and with spaces of affine functions Ac (S1) and Ac (S2) having the same density character, but which are not affinely homeomorphic. Keywords: Poulsen simplex, projective limit, Helly space
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