duals of convex cones

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# duals of convex cones

Submitted by josephkittinger on Mon, 03/26/2012 - 18:14

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Hello Everyone,

Is R^n the only convex cone (closed or not) in R^n whose dual is {0}?

Thanks! And sorry if that's a really trivial question.

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## Versions

(v1) by josephkittinger 2012-03-26

## Re: duals of convex cones

Yes, the dual of the dual of a convex cone is it closure. Since the dual of {0} is R^n any convex cone (closed or not) in R^n whose dual is {0} has R^n as it closure, and the only one convex cone in that condition is the R^n.