相关论文: Hofmann-Mislove through the Lenses of Priestley

We give an alternative, more geometric, proof of the well-known Joyal-Tierney Theorem in locale theory by utilizing Priestley duality for frames.

We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other things, this involves consideration of various morphisms…

Priestley duality has diverse applications in various branches of mathematics. In this survey, we discuss its usefulness in pointfree topology. This is done by providing Priestley perspective on several key notions, including spatiality,…

We first present a Priestley-style dualitiy for the classes of algebras that are the algebraic counterpart of some congruential, finitary and filter-distributive logic with theorems. Then we analyze which properties of the dual spaces…

There are several prominent duality results in pointfree topology. The Hofmann-Lawson duality establishes that the category of continuous frames is dually equivalent to the category of locally compact sober spaces. This restricts to a dual…

We prove the Lefschetz duality for intersection (co)homology in the framework of $\partial$-pesudomanifolds. We work with general perversities and without restriction on the coefficient ring.

This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.

We develop a new duality for distributive and implicative meet semi-lattices. For distributive meet semi-lattices our duality generalizes Priestley's duality for distributive lattices and provides an improvement of Celani's duality. Our…

We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial…

There are numerous generalizations of the celebrated Priestley duality for bounded distributive lattices to the non-distributive setting. The resulting dualities rely on an earlier foundational work of such authors as Nachbin,…

We prove versions of the spectral adjunction, a Stone-type duality and Hofmann-Lawson duality for locally small spaces with bounded continuous mappings.

In natural duality theory, the piggybacking technique is a valuable tool for constructing dualities. As originally devised by Davey and Werner, and extended by Davey and Priestley, it can be applied to finitely generated quasivarieties of…

We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding…

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

We give a short proof of the duality theorem for the reduced $L_p$-cohomology of a complete oriented Riemannian manifold.

Using Dold--Puppe category approach to the duality in topology, we prove general duality theorem for the category of motives. As one of the applications of this general result we obtain, in particular, a generalization of…

A description of dual non-Abelian duality is given, based on the notion of the Drinfeld double. The presentation basically follows the original paper \cite{KS2}, written in collaboration with P. \v Severa, but here the emphasis is put on…

We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.

We introduce a general framework for generating dualities between categories of partial orders and categories of ordered Stone spaces; we recover in particular the classical Priestley duality for distributive lattices and establish several…

We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincar\'e Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working…