In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally functions.

Article history: Received 17 July 2008 Received in revised form 6 October 2009 MSC: primary 54D20 secondary 54E30, 54E35, 54F05

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 ...