Abstract
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 nonempty player) in the strong Choquet game Ch (X); the existence of a stationary winning strategy for player α in Ch (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.
Original language | English |
---|---|
Pages (from-to) | 445-458 |
Number of pages | 14 |
Journal | Topology and its Applications |
Volume | 155 |
Issue number | 5 |
DOIs | |
State | Published - Jan 15 2008 |
Keywords
- Base of countable order
- Choquet completeness
- Co-compact space
- Domain representable
- Moore space
- Motonically complete base of countable order
- Normality in Moore spaces
- Rudin complete
- Scott-domain representable
- Stationary strategy
- Strong Choquet game
- Čech-complete