Geodesic
On hyperplanes and semispaces in max–min convex geometry
Kybernetika, Tome 46 (2010) no. 3, pp. 548-557 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The concept of separation by hyperplanes and halfspaces is fundamental for convex geometry and its tropical (max-plus) analogue. However, analogous separation results in max-min convex geometry are based on semispaces. This paper answers the question which semispaces are hyperplanes and when it is possible to “classically” separate by hyperplanes in max-min convex geometry.
The concept of separation by hyperplanes and halfspaces is fundamental for convex geometry and its tropical (max-plus) analogue. However, analogous separation results in max-min convex geometry are based on semispaces. This paper answers the question which semispaces are hyperplanes and when it is possible to “classically” separate by hyperplanes in max-min convex geometry.
Classification : 08A72, 14T05, 52A01, 52A30
Keywords: tropical convexity; fuzzy algebra; separation 
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     title = {On hyperplanes and semispaces in max{\textendash}min convex geometry},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010_46_3_a17/}
}
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Nitica, Viorel; Sergeev, Sergeĭ. On hyperplanes and semispaces in max–min convex geometry. Kybernetika, Tome 46 (2010) no. 3, pp. 548-557. http://geodesic.mathdoc.fr/item/KYB_2010_46_3_a17/

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