  We prove the Cartan and Choquet properties for the fine topology on a
complete metric space equipped with a doubling measure supporting a
$p$-Poincar\'e inequality, $1 < p< \infty$. We apply these key tools to
establish a fine version of the Kellogg property, characterize finely
continuous functions by means of quasicontinuous functions, and show that
capacitary measures associated with Cheeger supersolutions are supported by the
fine boundary of the set.
