  Given a sample from some unknown continuous density
$f:\mathbb{R}\to\mathbb{R}$, we construct adaptive confidence bands that are
honest for all densities in a "generic" subset of the union of $t$-H\"older
balls, $0<t\le r$, where $r$ is a fixed but arbitrary integer. The exceptional
("nongeneric") set of densities for which our results do not hold is shown to
be nowhere dense in the relevant H\"older-norm topologies. In the course of the
proofs we also obtain limit theorems for maxima of linear wavelet and kernel
density estimators, which are of independent interest.
