**
Journal of Convex Analysis, Vol. 6, No. 2, pp. 395-398 (1999)
**

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

##
J. Bair and J. C. Dupin

University of Liege, FEGSS, 7 bd du Rectorat, B31, 4000 Liege, Belgium, j.bair@ulg.ac.be and University of Valenciennes, Department of Mathematics, BP 311, 59304 Valenciennes-Cedex, France

**Abstract:** For an arbitrary non-empty closed convex set $A$ in $\mathbb{R}^n$, we prove that the polar of the difference between the barrier cone $\mathbb{B}(A)$ and its interior $\text{int } \mathbb{B} (A)$ coincides with the recession cone $0^+ (\text{cl } \mathbb{G}(A))$ of the closure of the cover $\mathbb{G}(a)$.

**Keywords:** convex set, barrier cone, recession cone, cover, polar cone

**Classification (MSC2000):** 52A20

**Full text of the article:**

[Previous Article] [Contents of this Number]

*
© 1999--2000 ELibM for
the EMIS Electronic Edition
*