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Minimal pairs of compact convex sets

Diethard PallaschkeRyszard Urbański — 2004

Banach Center Publications

Pairs of compact convex sets naturally arise in quasidifferential calculus as sub- and superdifferentials of a quasidifferentiable function (see Dem86). Since the sub- and superdifferentials are not uniquely determined, minimal representations are of special importance. In this paper we give a survey on some recent results on minimal pairs of closed bounded convex sets in a topological vector space (see PALURB). Particular attention is paid to the problem of characterizing minimal representatives...

Minimal pairs of bounded closed convex sets as minimal representations of elements of the Minkowski-Rådström-Hörmander spaces

Jerzy GrzybowskiDiethard PallaschkeRyszard Urbański — 2009

Banach Center Publications

The theory of minimal pairs of bounded closed convex sets was treated extensively in the book authored by D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets. In the present paper we summarize the known results, generalize some of them and add new ones.

Algebraic Separation and Shadowing of Arbitrary Sets

Jerzy GrzybowskiDiethard PallaschkeRyszard Urbański — 2013

Commentationes Mathematicae

In this paper we consider a generalization of the separation technique proposed in [10,4,7] for the separation of finitely many compact convex sets A i , i I by another compact convex set S in a locally convex vector space to arbitrary sets in real vector spaces. Then we investigate the notation of shadowing set which is a generalization of the notion of separating set and construct separating sets by means of a generalized Demyanov-difference in locally convex vector spaces.

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