A note on Krein-Milman theorem

Hubert Przybycień

doi:10.56754/0719-0646.2703.653

DOI:

https://doi.org/10.56754/0719-0646.2703.653

Abstract

In this note, we generalize a well-known theorem of Krein and Milman concerning the closed convex envelope of the extremal points of a compact convex set in a topological vector space to the case of an abstract convexity notion in a topological space with a convex structure defined on it. We also introduce some notions that will be useful to describe these generalizations.

Keywords

Convex sets , extremal points , Krein-Milman theorem

Mathematics Subject Classification:

52A07 , 52A30

Hubert Przybycień Faculty of Mathematics and Natural Sciences UJK, ul. Uniwersytecka 7, 25-406 Kielce, Poland. https://orcid.org/0000-0002-7125-6113

Pages: 653–658
Date Published: 2025-12-23
Vol. 27 No. 3 (2025)

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