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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…
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…
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 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…