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Arcwise Connectedness of Efficient Sets

Commun. Math. Anal.
Volume 10, Number 2 (2011), 1 - 17

Arcwise Connectedness of Efficient Sets

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Abstract

Let E be a topological vector space and C a pointed closed convex cone. For a set Q in E we prove arcwise connectedness of the efficient point set Max(Q|C) between any two points of a closed set MMax(Q|C) with a compact closed convex hull and having certain additional property. An application to a class of non-convex in general sets is given. The method generalizes the one from [6] concerning compact convex sets and allows also for such sets to obtain a more general result.