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Journal of Convex Analysis 06 (1999), No. 2, 395--398
Copyright Heldermann Verlag 1999

The Barrier Cone of a Convex Set and the Closure of the Cover

J. Bair
FEGSS, Université de Liège, 7 bd du Rectorat, 4000 Liège, Belgium

J. C. Dupin
Dép. de Mathématiques, Université de Valenciennes, 59304 Valenciennes, France

For an arbitrary non-empty closed convex set A in Rn, we prove that the polar of the difference between the barrier cone B(A) and its interior int(B(A)) coincides with the recession cone 0+(cl(G(A))) of the closure of the cover G(a).

Keywords: Convex set, barrier cone, recession cone, cover, polar cone.

MSC: 52A20

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