Ideal completion and Stone representation of ideal-distributive ordered sets
نویسندگان
چکیده
منابع مشابه
Ideal extensions of ordered sets
The ideal extensions of semigroups—without order—have been first considered by Clifford (1950). In this paper, we give the main theorem of the ideal extensions for ordered sets. If P , Q are disjoint ordered sets, we construct (all) the ordered sets V which have an ideal P ′ which is isomorphic to P , and the complement of P ′ in V is isomorphic toQ. Conversely, we prove that every extension of...
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1. Introduction Stone, in [8], developed for distributive lattices a representation theory generalizing that for Boolean algebras. This he achieved by topologizing the set X of prime ideals of a distributive lattice A (with a zero element) by taking as a base {P a : aeA} (where P a denotes the set of prime ideals of A not containing a), and by showing that the map a i-> P a is an isomorphism re...
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The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...
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It is shown that Matet’s characterization ([9]) of the Ramsey property relative to a selective co-ideal H, in terms of games of Kastanas ([6]), still holds if we consider semiselectivity ([3]) instead of selectivity. Moreover, we prove that a co-ideal H is semiselective if and only if Matet’s game-theoretic characterization of the H-Ramsey property holds. This lifts Kastanas’s characterization ...
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the starting point of this paper is given by priestley’s papers, where a theory of representation of distributive lattices is presented. the purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. in this way, some results of priestley’s papers are extended. in the main theorem, we show that the category of finite fuzzy priestley space...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1992
ISSN: 0166-8641
DOI: 10.1016/0166-8641(92)90083-c