  If NONEMPTY has a winning strategy against EMPTY in the Choquet game on a
space, the space is said to be a Choquet space. Such a winning strategy allows
NONEMPTY to consider the entire finite history of previous moves before making
each new move; a stationary strategy only permits NONEMPTY to consider the
previous move by EMPTY. We show that NONEMPTY has a stationary winning strategy
for every second countable T1 Choquet space. More generally, NONEMPTY has a
stationary winning strategy for any T1 Choquet space with an open-finite basis.
  We also study convergent strategies for the Choquet game, proving the
following results. (1) A T1 space X is the open image of a complete metric
space if and only if NONEMPTY has a convergent winning strategy in the Choquet
game on X. (2) A T1 space X is the compact open image of a metric space if and
only if X is metacompact and NONEMPTY has a stationary convergent strategy in
the Choquet game on X. (3) A T1 space X is the compact open image of a complete
metric space if and only if X is metacompact and NONEMPTY has a stationary
convergent winning strategy in the Choquet game on X.
