Abstract
It is proved that if the nonempty intersection of bounded closed convex sets A \ B is contained in (A u F) ( (B u F) and one of the following holds true: (i) the space X is less-than-three dimensional, (ii) A ( B is convex, (iii) F is a one-point set, then A \ B A u F or A \ B B u F (Theorems 2 and 3). Moreover, under some hypotheses the characterization of A and B such that A \ B is a summand of A ( B is given (Theorem 3). In this paper we consider the inclusion A\B (AuF)((B uF) which plays a central role in proving criterion of convex minimality of pairs of bounded closed convex sets (12), (13). Minimal pairs of compact convex sets were investigated in a series of papers (2), (4), (5), (10), (12), and others. Pairs of compact convex sets naturally arise in quasidierential
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