1 citations · 1 across the 10 of their papers we have counts for
10 papers
An overlooked weakening of perfect normality: Perfect regularity in spaces and locales
Ana Belén Avilez, Guram Bezhanishvili, Joanne Walters-Wayland
We introduce the notion of perfect regularity as an appropriate weakening of perfect normality, both for spaces and locales. Various characterizations are given, using Dedekind-Mac…
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…
Degrees of join-distributivity via Bruns-Lakser towers
G. Bezhanishvili, F. Dashiell, M. A. Moshier +1
We utilize the Bruns-Lakser completion to introduce Bruns-Lakser towers of a meet-semilattice. This machinery enables us to develop various hierarchies inside the class of bounded…
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 i…
Semilattice base hierarchy for frames and its topological ramifications
G. Bezhanishvili, F. Dashiell, A. Razafindrakoto +1
We develop a hierarchy of semilattice bases (S-bases) for frames. For a given (unbounded) meet-semilattice , we analyze the interval in the coframe of sublocales of the frame of…
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…