  The Mar\'echal topology, also called the Effros-Mar\'echal topology, is a
natural topology one can put on the space of all von Neumann subalgebras of a
given von Neumann algebra. It is a result of Mar\'echal from 1973 that this
topology is Polish as soon as the ambient algebra has separable predual, but
the sketch of proof in her research announcement appears to have a small gap.
Our main goal in this paper is to fill this gap by a careful look at the
topologies one can put on the space of weak-$*$ closed subspaces of a dual
space. We also indicate how Michael's selection theorem can be used as a step
towards Mar\'echal's theorem, and how it simplifies the proof of an important
selection result of Haagerup and Winsl{\o}w for the Mar\'echal topology. As an
application, we show that the space of finite von Neumann algebras is
$\mathbf\Pi^0_3$-complete.
