
Journal of Convex Analysis 28 (2021), No. 4, [final page numbers not yet available] 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. 