  Let $\Psi$ be the projectivization (i.e., the set of one-dimensional vector
subspaces) of a vector space of dimension $\ge 3$ over a field. Let $H$ be a
closed (in the pointwise convergence topology) subgroup of the permutation
group $\mathfrak{S}_{\Psi}$ of the set $\Psi$. Suppose that $H$ contains the
projective group and an arbitrary self-bijection of $\Psi$ transforming a
triple of collinear points to a non-collinear triple. It is well-known from
\cite{KantorMcDonough} that if $\Psi$ is finite then $H$ contains the
alternating subgroup $\mathfrak{A}_{\Psi}$ of $\mathfrak{S}_{\Psi}$.
  We show in Theorem \ref{density} below that $H=\mathfrak{S}_{\Psi}$, if
$\Psi$ is infinite.
