2 citations · 3 across the 8 of their papers we have counts for
8 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…
McKinsey-Tarski algebras and Raney extensions
Guram Bezhanishvili, Ranjitha Raviprakash, Anna Laura Suarez +1
We introduce the notion of Raney morphism between MT-algebras and show that the resulting category is equivalent to the category of Raney extensions. This is done by generalizing t…
The Funayama envelope as the -hull of a frame
Guram Bezhanishvili, Ranjitha Raviprakash, Anna Laura Suarez +1
We introduce proximity morphisms between MT-algebras and show that the resulting category is equivalent to the category of frames. This is done by utilizing the Funayama envelope o…
On Isbell's Density Theorem for bitopological pointfree spaces II
M. Andrew Moshier, Imanol Mozo Carollo, Joanne Walters-Wayland
With the aim of studying subspaces in pointfree bitopology, we characterize extremal epimorphism in biframes and show that a smallest dense one always exists, providing an analogue…
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…
Subfitness in distributive (semi)lattices
Guram Bezhanishvili, James Madden, M. Andrew Moshier +2
We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show…
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…