  Filtrations are certain transfinite sequences of topologies increasing in
strength and interpolating between two given topologies $\sigma$ and $\tau$,
with $\tau$ being stronger than $\sigma$. We prove general results on
stabilization at $\tau$ of filtrations interpolating between $\sigma$ and
$\tau$. These topological results involve an interplay between $\kappa$-Borel
sets with respect to the topology $\sigma$ and $\kappa$-Baireness of the
topology $\tau$.
