  We describe some sufficient conditions, under which smooth and compactly
supported functions are or are not dense in the fractional Sobolev space
$W^{s,p}(\Omega)$ for an open, bounded set $\Omega\subset\mathbb{R}^{d}$. The
density property is closely related to the lower and upper Assouad codimension
of the boundary of $\Omega$. We also describe explicitly the closure of
$C_{c}^{\infty}(\Omega)$ in $W^{s,p}(\Omega)$ under some mild assumptions about
the geometry of $\Omega$. Finally, we prove a variant of a fractional order
Hardy inequality.
