Scott-representability of some spaces of Tall and Mǐskin
نویسندگان
چکیده
In this paper we show that a variation of a technique of Mǐskin and Tall yields a cocompact completely regular Moore space that is Scott-domain-representable and has a closed Gδ-subspace that is not Scott-domain-representable. This clarifies the general topology of Scott-domain-representable spaces and raises additional questions about Scott-domain representability in Moore spaces. 2000 AMS Classification: Primary 54E30; Secondary 54D70,06B35, 06F30, 54H12, 54D20
منابع مشابه
Domain Representability and the Choquet Game in Moore and BCO-spaces
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 Ch...
متن کاملQuantale-valued fuzzy Scott topology
The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...
متن کاملL-CONVEX SYSTEMS AND THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS
The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.
متن کاملDomain-Representability of Certain Complete Spaces
In this paper we show that three major classes of topological spaces are domain-representable, i.e., homeomorphic to the space of maximal elements of some domain (=continuous dcpo) with the relative Scott topology. The three classes are: T3 subcompact spaces, strongly α-favorable spaces with a Gδ-diagonal or with a base of countable order, and complete quasi-developable T3-spaces. It follows th...
متن کاملOn the representation of preference orders on sequence spaces
A set of su¢ cient conditions for representability of preference orders on real sequence spaces is analyzed. In particular, monotonicity and continuity of the order is not assumed. Two applications are worked out to demonstrate how such a result might be useful. Jel Codes: C60, D01
متن کامل