
Journal of Convex Analysis 28 (2021), No. 4, 12811291 Copyright Heldermann Verlag 2021 Stability of Closedness of Closed Convex Sets under Linear Mappings Si Tiep Dinh Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam dstiep@math.ac.vn TienSon Pham Department of Mathematics, Dalat University, Dalat, Vietnam sonpt@dlu.edu.vn We study the problem of when the linear image of a fixed closed convex subset X of R^{n} is closed. Specifically, we improve results of J. M. Borwein and W. B. Moors [Stability of closedness of convex cones under linear mappings I, J. Convex Analysis 16 (2009) 699705; Stability of closedness of convex cones under linear mappings II, J. Nonlinear Analysis Optim. 1 (2010) 17] by showing that for almost all linear mappings T from R^{n} into R^{m}, not only T(X) is closed, but there is also an open neighborhood of T whose members also preserve the closedness of X. Keywords: Asymptotic cone, closedness, convex cone, convex set, linear mapping, stability, sigmaporosity. MSC: 47N10; 90C25, 90C22. [ Fulltextpdf (116 KB)] for subscribers only. 