  For a metrizable space, we consider the space of all metrics generating the
same topology of the metrizable space, and this space of metrics is equipped
with the supremum metric. In this paper, for every metrizable space, we
establish that the space of metrics on the metrizable space is Baire. We also
show that the set of all complete metrics is comeager in the space of metrics.
Moreover, we investigate non--Archimedean analogues of these results.
