  We construct a separate continuous function
$f\colon\mathbb{Q}\times\mathbb{Q}\to[0,1] $ and a dense subset $D\subseteq
\mathbb{Q}\times\mathbb{Q}$ such that $f[D]$ is not dense in
$f[\mathbb{Q}\times\mathbb{Q}]$, in other words, $f$ is separate continuous and
not feebly (somewhat) continuous.
