  We consider the $(1,2)$-Sobolev space $W^{1,2}(U)$ on subsets $U$ in an
abstract Wiener space, which is regarded as a canonical Dirichlet space on $U$.
We prove that $W^{1,2}(U)$ has smooth cylindrical functions as a dense subset
if $U$ is $H$-convex and $H$-open. For the proof, the relations between
$H$-notions and quasi-notions are also studied.
