Thanks for pointing out. Is it okay now?

Yes, of course. Thanks for pointing out.

I knew only about the result by Kirszbrzun but not any further development.Here is what I would like to ask.Let $X$ be a real Banach sp,$Y$ a subspace of it and $f$ a 1-Lip map from $X$ to $\mathbb{R}$.Is it possible to get an extn of $f$ from $X$ to $\mathbb{R}$ with Lip constant 1? The case when $X$ is a metric sp and $Y$ a finite dim. subsp, the result follows from MR0737400(86a:46018).But let us assume $X=C(K)$,$K$ is cpt $T_2$(can assume metrizable also)and $Y=\{f:f|_D=0\}$ (ie an M-ideal) of $X$.Now can a real valued 1-Lip map from $Y$ necessarily has a similar extn ? Can it be unique ?

Okay, I mean a metrizable lctvs but not necessarily normed linear space.