  For a quantale ${\sf{V}}$, the category $\sf V$-${\bf Top}$ of
${\sf{V}}$-valued topological spaces may be introduced as a full subcategory of
those ${\sf{V}}$-valued closure spaces whose closure operation preserves finite
joins. In generalization of Barr's characterization of topological spaces as
the lax algebras of a lax extension of the ultrafilter monad from maps to
relations of sets, for ${\sf{V}}$ completely distributive,
${\sf{V}}$-topological spaces have recently been shown to be characterizable by
a lax extension of the ultrafilter monad to ${\sf{V}}$-valued relations. As a
consequence, ${\sf{V}}$-$\bf Top$ is seen to be a topological category over
$\bf Set$, provided that ${\sf{V}}$ is completely distributive. In this paper
we give a choice-free proof that ${\sf{V}}$-$\bf Top$ is a topological category
over $\bf Set$ under the considerably milder provision that ${\sf{V}}$ be a
spatial coframe. When ${\sf{V}}$ is a continuous lattice, that provision yields
complete distributivity of ${\sf{V}}$ in the constructive sense, hence also in
the ordinary sense whenever the Axiom of Choice is granted.
