A Topological Duality for Monotone Expansions of Semilattices
نویسندگان
چکیده
In this paper we provide a Stone style duality for monotone semilattices by using the topological developed in S. Celani, L.J. González (Appl Categ Struct 28:853–875, 2020) together with description of their canonical extension. As an application obtain characterization congruences means lower-Vietoris-type topologies.
منابع مشابه
Minimal Expansions of Semilattices
We determine the minimal extension of the sequence 〈0, 1, 1, . . . , 1, 2〉. This completes and extends the work of K. M. Koh, started in 1970, and solves Problem 15 in the survey on pnsequences and free spectra [GK92]. The results involve the investigation of some minimal expansions of semilattices.
متن کاملTopological Duality and Lattice Expansions Part I: A Topological Construction of Canonical Extensions
The two main objectives of this paper are (a) to prove topological duality theorems for semilattices and bounded lattices, and (b) to show that the topological duality from (a) provides a construction of canonical extensions of bounded lattices. The paper is the first of two parts. The main objective of the sequel [MJ2] is to establish a characterization of lattice expansions, i.e., lattices wi...
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We carry out a detailed comparison of the two topological dualities for distributive meet-semilattices studied by Celani [3] and by Bezhanishvili and Jansana [2]. We carry out such comparison, that was already sketched in [2], by defining the functors involved in the equivalence of both dual categories of distributive meet-semilattices.
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2022
ISSN: ['1572-9095', '0927-2852']
DOI: https://doi.org/10.1007/s10485-022-09690-0