论文标题
线性映射下闭合凸组闭合的稳定性
Stability of closedness of closed convex sets under linear mappings
论文作者
论文摘要
我们研究了固定封闭凸的连续线性图像$ x \ subset \ mathbb {r}^n $何时关闭的问题。具体而言，我们通过向所有人展示，除了最多最多的$σ$ porous套件外，我们改善了论文\ cite \ cite \ cite {borwein2009，borwein2009，borwein2010}。会员还保留了$ X的闭合度。
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 $σ$-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 $X.$
