exhaustion by compact sets

Let $U$ be an open set in $\\mathbbmss{R}^{n}$ (or a manifold with countable base). Then there exists a sequence of compact sets $K_{1},K_{2},\\ldots$ such that

	$\\displaystyle K_{i}$	$\\displaystyle\\subseteq$	$\\displaystyle\\operatorname{int}K_{i+1},\\quad i=1,2,\\ldots,$
	$\\displaystyle U$	$\\displaystyle=$	$\\displaystyle\\cup_{i=1}^{\\infty}K_{i},$

where “ $\\operatorname{int}$ ” denotes the topological interior. Such a sequence is called an exhaustion by compact setsfor $U$ .