# Riesz’ Lemma

Let $E$ be a normed space, $S\subset E$ a closed proper vector subspace, and $0<\alpha<1$. Then there is $x_{\alpha}\in E\setminus S$ such that $\|x_{\alpha}\|=1$ and $\|s-x_{\alpha}\|>\alpha$ for every $s\in S$.

Title Riesz’ Lemma RieszLemma 2013-03-22 14:56:11 2013-03-22 14:56:11 gumau (3545) gumau (3545) 6 gumau (3545) Theorem msc 15A03 msc 54E35