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arXiv · 1512.07275

Convexity and a Stone-type theorem for convex sets in abelian semigroup setting

Witold Jarczyk·Zsolt Páles
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Abstract

In this paper, two parallel notions of convexity of sets are introduced in the abelian semigroup setting. The connection of these notions to algebraic and to set-theoretic operations is investigated. A formula for the computation of the convex hull is derived. Finally, a Stone-type separation theorem for disjoint convex sets is established.

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Witold Jarczyk, Zsolt Páles. 2015-12-22. Convexity and a Stone-type theorem for convex sets in abelian semigroup setting. https://doi.org/10.1007/s00233-014-9613-0

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