7 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…
Pseudocomplementation in rings of continuous functions
Guram Bezhanishvili, Marcus Tressl
We study rings of real-valued continuous functions in terms of pseudocomplementation conditions on various lattices attached to their prime spectrum. We fully characterize pseudoco…
A new proof of Funayama's theorem
Guram Bezhanishvili, Wesley H. Holliday
Funayama proved that a lattice embeds into a complete Boolean algebra in such a way that all existing joins and meets are preserved if and only if the lattice satisfies the join-in…
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…
Dedekind-MacNeille and related completions: subfitness, regularity, and Booleanness
G. Bezhanishvili, F. Dashiell, M. A. Moshier +1
Completions play an important rôle for studying structure by supplying elements that in some sense ``ought to be." Among these, the Dedekind-MacNeille completion is of particular…