Friday, 9 August 2013

analysis - If $K'$ is the compact support of a $ℝ$-valued function on an open set $Ω⊆ℝ^d$, can we find a closed ball $K$ with $K⊆Ω$ and $K'⊆K$?

Let





  • $d\in\mathbb N$

  • $\Omega\subseteq\mathbb R^d$ be non-empty and open

  • $\phi:\Omega\to\mathbb R$ be continuous with compact support $\operatorname{supp}\phi$



Can we find a closed ball $K$ such that $K\subseteq\Omega$ and $K':=\operatorname{supp}\phi\subset K$?

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