We prove that if ZFC is consistent so is ZFC + "for any sequence
A_{n} of subsets of a Polish space (X,\tau)
there exists a separable metrizable topology \tau' on X with
Borel(X,\tau) subset of Borel(X,\tau'),
MEAGER(X,\tau') intersected with Borel(X,\tau) equal to
MEAGER(X,\tau) intersected with Borel(X,\tau),
and A_{n} Borel in \tau' for all n."
This is a category analogue of a theorem of Carlson on
the possibility of extending
Lebesgue measure to any countable collection of sets. A uniform
argument is presented, which gives a new proof of the latter as well.

Some consequences of these extension properties are also studied.

**Requires PROC-L.CLS file.**