Friday, 9 August 2013

analysis - If K is the compact support of a -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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