For a frame L, let XL be the Esakia space of L. We identify a special subset YL of XL
consisting of nuclear points of XL, and prove the following results:• L is spatial iff YL is dense …

There are several prominent duality results in pointfree topology. Hofmann–Lawson duality
establishes that the category of continuous frames is dually equivalent to the category of …

Completions play an important r\^ ole for studying structure by supplying elements that in
some sense``ought to be." Among these, the Dedekind-MacNeille completion is of particular …

We develop the theory of Krull dimension for S4-algebras and Heyting algebras. This leads
to the concept of modal Krull dimension for topological spaces. We compare modal Krull …

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Hofmann–Mislove through the lenses of Priestley | Semigroup Forum Skip to main content
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We use Priestley duality as a new tool to study maximal $ d $-spectra of arithmetic frames,
both with and without units. We pay special attention to when the maximal $ d $-spectrum is …

For a topological space X, let L (X) be the modal logic of X where□ is interpreted as interior
(and hence◇ as closure) in X. It was shown in [3] that the modal logics S4, S4. 1, S4. 2, S4 …

We present a contravariant adjunction between compact $ T_1 $-spaces and a class of
distributive lattices which recomprises key portions of Stone's duality and of Isbell's duality …

Connecting Priestley duality to Hofmann-Mislove-Stralka duality Page 1 Theory and
Applications of Categories, Vol. 41, No. 54, 2024, pp. 1937–1982. CONNECTING …