Domain Representability and the Choquet Game in Moore and BCO-spaces
نویسندگان
چکیده
In this paper we investigate the role of domain representability and Scott-domain representability in the class of Moore spaces and the larger class of spaces with a base of countable order. We show, for example, that in a Moore space, the following are equivalent: domain representability; subcompactness; the existence of a winning strategy for player α (= the non-empty player) in the strong Choquet game Ch(X); the existence of a stationary winning strategy for player α inCh(X); and Rudin completeness. We note that a metacompact Čech-complete Moore space described by Tall is not Scott-domain representable and also give an example of Čech-complete separable Moore space that is not co-compact and hence not Scott-domain representable. We conclude with a list of open questions.
منابع مشابه
Scott-representability of some spaces of Tall and Mǐskin
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