  We study the problem of existence of preduals of locally convex Hausdorff
spaces. We derive necessary and sufficient conditions for the existence of a
predual with certain properties of a bornological locally convex Hausdorff
space $X$. Then we turn to the case that $X=\mathcal{F}(\Omega)$ is a space of
scalar-valued functions on a non-empty set $\Omega$ and characterise those
among them which admit a special predual, namely a strong linearisation, i.e.
there are a locally convex Hausdorff space $Y$, a map $\delta\colon\Omega\to Y$
and a topological isomorphism $T\colon\mathcal{F}(\Omega)\to Y_{b}'$ such that
$T(f)\circ \delta= f$ for all $f\in\mathcal{F}(\Omega)$.
