Stability of closedness of convex cones under linear mappings
نویسندگان
چکیده
In this paper we reconsider the question of when the continuous linear image of a closed convex cone is closed in Euclidean space. In particular, we show that although it is not true that the closedness of the image is preserved under small perturbations of the linear mappings it is “almost” true that the closedness of the image is preserved under small perturbations, in the sense that, for “almost all” linear mappings from Rn into Rm if the image of the cone is closed then there is a small neighbourhood around it whose members also preserve the closedness of the cone. AMS (2002) subject classification: Primary 47N10 ; Secondary 90C25, 90C22.
منابع مشابه
Stability of closedness of convex cones under linear mappings II
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 σ-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. AMS (2002) s...
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