From Subcompact to Domain Representable
نویسندگان
چکیده
We introduce the property generalized subcompact and prove that subcompact implies generalized subcompact and that generalized subcompact implies domain representable. We develop a simplified characterization of domain representable. We also present an extension X of Debs’ space and prove that X is generalized subcompact but α does not have a stationary winning strategy in the Banach-Mazur game on X . A fortiori, subcompactness does not imply domain representability. We investigate whether Gδ subspaces of subcompact (generalized subcompact, domain representable) spaces are subcompact (generalized subcompact, domain representable). We show that the union of two domain representable subspaces is domain representable, and that a locally domain representable space is domain representable. Domain representable subcompact α-favorable Choquet complete Debs’ space domain theory MSC Primary 54E52 Secondary 54E50 54D70 54G20 06B15 Email address: [email protected], [email protected] (William Fleissner and Lynne Yengulalp) Preprint submitted to Elsevier October 31, 2013 From Subcompact to Domain Representable William Fleissner and Lynne Yengulalp Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, Department of Mathematics, University of Dayton, Dayton, Ohio 45469
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