3 citations · 5 across the 9 of their papers we have counts for
9 papers
When is double negation Scott continuous?
Guram Bezhanishvili, Sebastian D. Melzer
Let be the frame of opens of a -space . We prove that if is sober and , then the double negation nucleus on is Scott continuous iff is discrete. It fol…
Maximal d-spectra and locally compact Hausdorff spaces
G. Bezhanishvili, P. Bhattacharjee, S. D. Melzer +1
It is an interesting open problem whether every compact Hausdorff space can be realized as the maximal -spectrum of an arithmetic frame. We approach this problem by generalizing…
A choice-free approach to Wallman compactifications
Sebastian D Melzer, Cerene Rathilal, Ranjitha Raviprakash
The classical Wallman compactification of a -space and the Stone--Čech compactification of a completely regular space rely on choice principles. We show that, by representing…
Priestley perspective on pointfree topology
Guram Bezhanishvili, Sebastian D. Melzer
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…
Local compactness does not always imply spatiality
G. Bezhanishvili, S. D. Melzer, R. Raviprakash +1
It is a well-known result in pointfree topology that every locally compact frame is spatial. Whether this result extends to MT-algebras (McKinsey-Tarski algebras) was an open probl…
Maximal -spectra via Priestley duality
G. Bezhanishvili, P. Bhattacharjee, S. D. Melzer
We use Priestley duality as a new tool to study maximal -spectra of arithmetic frames, both with and without units. We pay special attention to when the maximal -spectrum is…
Algebraic Frames in Priestley duality
G. Bezhanishvili, S. Melzer
We characterize Priestley spaces of algebraic, arithmetic, coherent, and Stone frames. As a corollary, we derive the well-known dual equivalences in pointfree topology involving va…
Deriving dualities in pointfree topology from Priestley duality
G. Bezhanishvili, S. Melzer
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 categor…
Hofmann-Mislove through the Lenses of Priestley
G. Bezhanishvili, S. Melzer
We use Priestley duality to give a new proof of the Hofmann-Mislove Theorem.