Abstract:
Classically it is known that any set with packing dimension less than
1 is meager in the sense of Baire category. We establish a
resource-bounded extension: if a class X has Δ-strong
dimension less than 1, then X is Δ-meager. This has the
applications of explaining some of Lutz's simultaneous
Δ-meager, Δ-measure 0 results and providing a new proof
of a Gu's strong dimension result on infinitely-often classes.