We study the problem of when the continuous linear image of a fixed closed convex set $X \subset\mathbb{ R}^n$ is closed. Specifically, we improve the main results in the papers \cite{ Borwein2009, Borwein2010} by showing that for all, except for at most a $\sigma$-porous set, of the linear mappings $T$ from $\mathbb{ R}^n$ into $\mathbb{ R}^m,$ not only $T(X)$ is closed, but there is also an open neighborhood of $T$ whose members also preserve the closedness of $X.$
Categories: math.OC math.FA