6 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--Äech compactification of a completely regular space rely on choice principles. We show that, by representing…
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…
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…