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Dawson, Robert

Common supports of families of sets. (English) Zbl 0813.52001

Geom. Dedicata 51, No. 1, 1-13 (1994).
For a family \(A\) of closed bounded convex sets of a Banach space sufficient conditions are given for the existence of a closed hyperplane which supports each member of \(A\) in such a way that all of them are contained in the same closed halfspace. One of the sufficient conditions is that all members of \(A\) surround a flat \(F\), which means that \(F\) intersects the convex hull of all members of \(A\) but not of any subfamily. Also separating common supports are considered.
Reviewer: E.Heil (Darmstadt)

MSC:

52A07 Convex sets in topological vector spaces (aspects of convex geometry)
52A35 Helly-type theorems and geometric transversal theory

Keywords:

support; separation; bounded convex sets; Banach space; hyperplane
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\textit{R. Dawson}, Geom. Dedicata 51, No. 1, 1--13 (1994; Zbl 0813.52001)
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References:

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