  In 2009, Caramello proved that each topos has a largest dense subtopos whose
internal logic satisfies De Morgan law (also known as the law of the weak
excluded middle). This finding implies that every locale has a largest dense
extremally disconnected sublocale, referred to as its DeMorganization. In this
paper, we take the first steps in exploring the DeMorganization in the localic
context, shedding light on its geometric nature by showing that it is always a
fitted sublocale and by providing a concrete description. The main result of
the paper is that for any metrizable locale (without isolated points), its
DeMorganization coincides with its Booleanization. This, in particular, implies
that any extremally disconnected metric locale (without isolated points) must
be Boolean, generalizing a well-known result for topological spaces to the
localic setting.
