Abstract

B-convexity was defined by the author and C. D. Horvath [B-convexity, Optimization 53(2) (2004) 103–127] as a suitable Kuratowski-Painlevé upper limit of linear convexities over a finite dimensional Euclidean vector space. Recently, an alternative formulation over the whole Euclidean vector space was proposed [W. Briec, Some remarks on an idempotent and non-associative convex structure, Journal of Convex Analysis 22 (2015) 259–289]. In this paper a convex separation framework is proposed as well as some extension of known results established over posets. We first analyze the algebraic properties of some class of subsets characterized by a suitable notion of dual form. Along this line some extended separation results are established by considering the Kuratowski-Painlevé limit of a sequence of linear halfspaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Walter Briec

University of Perpignan, 52 avenue Villeneuve, 66000 Perpignan, France

briec@univ-perp.fr

Keywords

  • Idempotence
  • semilattices
  • generalized convexity
  • B-convexity

Mathematics Subject Classification

06D50, 32F17

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Suggested citation

W. Briec. “Separation Properties in some Idempotent and Symmetrical Convex Structure.” Journal of Convex Analysis 24 (2017), No. 4, 1143–1168. https://doi.org/10.68381/jca24067

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.