  It is well known that every (real or complex) normed linear space $L$ is
isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here
$X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued
linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by
the Banach-Alaoglu theorem. We prove that the compact Hausdorff space $X$ can
indeed be chosen to be the Stone-Cech compactification of $L^*\setminus\{0\}$,
where $L^*\setminus\{0\}$ is endowed with the supremum norm topology.
