# duals of convex cones

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.

### 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.