Stability of closedness of convex cones under linear mappings II

Abstract

In this paper we revisit the question of when the continuous linear image of a fixed closed convex cone K is closed. Specifically, we improve the main result of [3] by showing that for all, except for at most a s-porous set, of the linear mappings T from Rn into Rm, not only is T(K) closed, but there is also a neighbourhood around T whose members also preserve the closedness of K.