Show that ‘the closure operators cannot be omitted’ from the formulas above in general. That is, one might have, for suitable pairs of closed convex cones in duality (C,C)˜ and (D, D)˜ in Rn, C + D =...

Show that ‘the closure operators cannot be omitted’ from the formulas above

in general. That is, one might have, for suitable pairs of closed convex cones in

duality (C,C)˜ and (D, D)˜ in Rn,

C + D = (C˜ ∩ D)˜ ◦

and

(CM˜ )

◦ = MC.