  We study two classes of spaces whose points are filters on partially ordered
sets. Points in MF spaces are maximal filters, while points in UF spaces are
unbounded filters. We give a thorough account of the topological properties of
these spaces. We obtain a complete characterization of the class of countably
based MF spaces: they are precisely the second-countable T_1 spaces with the
strong Choquet property. We apply this characterization to domain theory to
characterize the class of second-countable spaces with a domain representation.
