Let $X=\mathrm{Conv}(\mathbf R)$, the collection of all convergent sequences in $\mathbf{R}$. Is the normed space $(X,\|\cdot\|_\infty)$ complete?
How to prove that the space of convergent sequences is complete?
6
$\begingroup$
functional-analysis
banach-spaces
-
8What did you try? – 2012-09-04