Closedness of cones

Stability of closedness of convex cones under linear mappings

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 “al...

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...

LωH-closedness in Lω-spaces

In this paper, the concepts of LωH-sets and LωH-closed spaces are proposed in Lω-spaces by means of (αω)−-remote neighborhood family. The characterizations of LωH-sets and LωH-closed spaces are systematically discussed. Some important properties of LωH-closed spaces, such as the LωH-closed spaces is ω-regular closed hereditary, arbitrarily multiplicative and preserving invariance under almost (...

Closedness properties in ex-identification

In this paper we investigate in which cases unions of identi$able classes are also necessarily identi$able. We consider identi$cation in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identi$cation types still have features resembling closedness. For each of them we $nd n such that (1) if every union of n − 1 classes out of U1; : : : ; Un is ide...

On Closedness of Orbits of Algebraic Groups