We observe that if
is a compatible totally bounded quasi-uniformity on a T0-space (X,
), then the bicompletion
of (X,
) is a strongly sober, locally quasicompact space. It follows that the b-closure S of (X,
) in
is homeomorphic to the sobrification of the space (X,
). We prove that S is equal to
if and only if (X,
) is a core-compact space in which every ultrafilter has an irreducible convergence set and
is the coarsest quasi-uniformity compatible with
. If
is the Pervin quasi-uniformity on X, then S is equal to
if and only if X is hereditarily quasicompact, or equivalently,
is the Pervin quasi-uniformity on
.