  We prove that any continuous mapping $f:E\to Y$ on a completely metrizable
subspace $E$ of a perfect paracompact space $X$ can be extended to a Lebesgue
class one mapping $g:X\to Y$ (i.e. for every open set $V$ in $Y$ the preimage
$g^{-1}(V)$ is an $F_\sigma$-set in $X$) with values in an arbitrary
topological space $Y$.
