From subcompact to domain representable

摘要

We introduce the property generalized subcompactness and prove that subcompactness implies generalized subcompactness and that generalized subcompactness implies domain representability. We develop a simplified characterization of domain representability. We present an extension X of Debs' space and prove that X is generalized subcompact but alpha does not have a stationary winning strategy in the Banach-Mazur game on X. A fortiori, domain representability does not imply subcompactness. We investigate whether G(delta) subspaces of subcompact (generalized subcompact, domain representable) spaces are subcompact (generalized subcompact, domain representable). We show that Cech complete generalized ordered spaces are subcompact. We show that the union of two domain representable subspaces is domain representable, and that a locally domain representable space is domain representable. (C) 2015 Elsevier B.V. All rights reserved.