  This paper deals with a property which is equivalent to generalised-lushness
for separable spaces. It thus may be seemed as a geometrical property of a
Banach space which ensures the space to have the Mazur-Ulam property. We prove
that if a Banach space $X$ enjoys this property if and only if $C(K,X)$ enjoys
this property. We also show the same result holds for $L_\infty(\mu,X)$ and
$L_1(\mu,X)$.
