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arXiv · 2001.07896

Stability of closedness of closed convex sets under linear mappings

Si Tiep Dinh·Tien Son Pham
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Abstract

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 $X.$

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Si Tiep Dinh, Tien Son Pham. 2020-01-22. Stability of closedness of closed convex sets under linear mappings. https://arxiv.org/abs/2001.07896

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