The Vietoris functor and modal operators on rings of continuous functions
نویسندگان
چکیده
We introduce an endofunctor H on the category baℓ of bounded archimedean ℓ-algebras and show that there is a dual adjunction between Alg(H) algebras for Coalg(V) coalgebras Vietoris V compact Hausdorff spaces. prove Gelfand duality lifts to equivalence full reflective subcategory Algu(H) Alg(H). provide alternate view by introducing Hu consisting uniformly complete objects showing Alg(Hu) isomorphic Algu(H). On one hand, these results generalize those [1], [19] Stone other they alternate, more categorical proof recent result [6].
منابع مشابه
Modal logic and the Vietoris functor
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For a topological space X, and a topological ring A, let C(X,A) be the ring of all continuous functions from X into A under the pointwise multiplication. We show that the theorem "there is a completely regular space Y associated with a given topological space X such that C(Y,R) is isomorphic to C(X,R)" may be extended to a fairly large class of topologlcal rings, and that, in the study of algeb...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2022
ISSN: ['0168-0072', '1873-2461']
DOI: https://doi.org/10.1016/j.apal.2021.103029