Representability of BCO and Moore spaces
by
David Lutzer
College of William and Mary, Williamsburg, VA
Coauthors: Hal Bennett and Mike Reed

This paper studies domain-representability and Scott-domain representability in Moore spaces and in the BCO-spaces of Wicke and Worrell. We show that for a regular BCO space X, the following are equivalent: domain representability, subcompactness, the existence of a stationary winning strategy for player a in the Choquet game Ch(X), the existence of a winning strategy for player a in Ch(X), and the existence of a monotonically complete BCO for X. We also examine Scott-domain representability of Moore spaces, presenting a class of Scott-domain representable Moore spaces that contains many of the classical examples of complete Moore spaces, and showing that a space of F.D Tall is Moore-complete and Cech-complete but not Scott-domain representable. This answers several questions in the literature.

Date received: February 13, 2006