An interval version of separation by semispaces in max-min convexity |
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Authors: | Viorel Nitica Sergei? Sergeev |
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Affiliation: | a Department of Mathematics, West Chester University, PA 19383, USA b Institute of Mathematics, P.O. Box 1-764, Bucharest, Romania c University of Birmingham, School of Mathematics, Watson Building, Edgbaston B15 2TT, UK |
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Abstract: | In this paper, we study separation of a closed box from a max-min convex set by max-min semispaces. This can be regarded as an interval extension of the known separation results. We give a constructive proof of the separation in the case when the box satisfies a certain condition, and we show that the separation is never possible when the condition is not satisfied. We also study the separation of two max-min convex sets by a box and by a box and a semispace. |
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Keywords: | Primary: 52A01 Secondary: 52A20 52A80 08A72 |
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