Journal of Convex Analysis 25 (2018), No. 4, 1319--1334
Copyright Heldermann Verlag 2018
Reduced and Minimally Convex Pairs of Sets
Jerzy Grzybowski
Faculty of Mathematics and Computer Science, Adam-Mickiewicz-University, Umultowska 87, 61-614 Poznan, Poland
jgrz@amu.edu.pl
Diethard Pallaschke
Institute of Operations Research, Karlsruhe Institute of Technology, Kaiserstr. 89, 76133 Karlsruhe, Germany
diethard.pallaschke@kit.edu
Hubert Przybycien
Faculty of Mathematics and Computer Science, Adam-Mickiewicz-University, Umultowska 87, 61-614 Poznan, Poland
hubert@amu.edu.pl
R. Urbanski
Faculty of Mathematics and Computer Science, Adam-Mickiewicz-University, Umultowska 87, 61-614 Poznan, Poland
rich@amu.edu.pl
In this paper algebraic properties of convex sets are studied. In the first section we present one of our main results which is an algebraic order cancellation law of convex sets. Then we study properties of convex pairs and reduced pairs mainly within the general frame of commutative semigroups which satisfy the order cancellation law.
Keywords: Quasidifferential, pairs of bounded closed convex sets, order cancellation law, minimal pairs, reduced pairs.
MSC: 52A07, 52A20, 26A27, 26B25
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