3 citations · 19 across the 44 of their papers we have counts for
17 papers · 1 filter
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…
Local compactness in MT-algebras
Guram Bezhanishvili, Ranjitha Raviprakash
In our previous work, we introduced McKinsey-Tarski algebras (MT-algebras for short) as an alternative pointfree approach to topology. Here we study local compactness in MT-algebra…
Vietoris endofunctor for closed relations and its de Vries dual
Marco Abbadini, Guram Bezhanishvili, Luca Carai
We generalize the classic Vietoris endofunctor to the category of compact Hausdorff spaces and closed relations. The lift of a closed relation is done by generalizing the construct…
McKinsey-Tarski Algebras: An alternative pointfree approach to topology
Guram Bezhanishvili, Ranjitha Raviprakash
McKinsey and Tarski initiated the study of interior algebras. We propose complete interior algebras as an alternative pointfree approach to topology. We term these algebras McKinse…
A New Proof of the Joyal-Tierney Theorem
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We give an alternative, more geometric, proof of the well-known Joyal-Tierney Theorem in locale theory by utilizing Priestley duality for frames.
Deriving dualities in pointfree topology from Priestley duality
G. Bezhanishvili, S. Melzer
There are several prominent duality results in pointfree topology. The Hofmann-Lawson duality establishes that the category of continuous frames is dually equivalent to the categor…
MacNeille completions of subordination algebras
Marco Abbadini, Guram Bezhanishvili, Luca Carai
-subordination algebras are a natural generalization of de Vries algebras. Recently it was proved that the category of -subordination a…
Remarks on Hyperspaces for Priestley Spaces
G. Bezhanishvili, J. Harding, P. J. Morandi
The Vietoris space of a Stone space plays an important role in the coalgebraic approach to modal logic. When generalizing this to positive modal logic, there is a variety of releva…
A generalization of de Vries duality to closed relations between compact Hausdorff spaces
Marco Abbadini, Guram Bezhanishvili, Luca Carai
Stone duality generalizes to an equivalence between the categories of Stone spaces and closed relations and of boolean algebr…
A new approach to the Katětov-Tong theorem
Guram Bezhanishvili, Patrick J. Morandi, Bruce Olberding
We give a new proof of the Katětov-Tong theorem. Our strategy is to first prove the theorem for compact Hausdorff spaces, and then extend it to all normal spaces. The key ingredien…
Modal operators on rings of continuous functions
Guram Bezhanishvili, Luca Carai, Patrick Morandi
It is a classic result in modal logic that the category of modal algebras is dually equivalent to the category of descriptive frames. The latter are Kripke frames equipped with a S…
The Frame of Nuclei of an Alexandroff Space
Francisco Ávila, Guram Bezhanishvili, Patrick Morandi +1
Let be the frame of open sets of a topological space , and let be the frame of nuclei of . For an Alexandroff space , we prove…
When is the frame of nuclei spatial: A new approach
Francisco Ávila, Guram Bezhanishvili, Patrick Morandi +1
For a frame , let be the Esakia space of . We identify a special subset of consisting of nuclear points of , and prove the following results: is sp…
Gelfand-Naimark-Stone duality for normal spaces and insertion theorems
G. Bezhanishvili, P. J. Morandi, B. Olberding
Gelfand-Naimark-Stone duality provides an algebraic counterpart of compact Hausdorff spaces in the form of uniformly complete bounded archimedean -algebras. In [4] we extende…
A generalization of Gelfand-Naimark-Stone duality to completely regular spaces
Guram Bezhanishvili, Patrick J. Morandi, Bruce Olberding
Gelfand-Naimark-Stone duality establishes a dual equivalence between the category of compact Hausdorff spaces and the category of un…
De Vries duality for normal spaces and locally compact Hausdorff spaces
Guram Bezhanishvili, Patrick J. Morandi, Bruce Olberding
By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras. In our recent article, we have extended de Vries duality to…
De Vries duality for compactifications and completely regular spaces
Guram Bezhanishvili, Patrick J. Morandi, Bruce Olberding
De Vries duality yields a dual equivalence between the category of compact Hausdorff spaces and a category of complete Boolean algebras with a proximity relation on them, known as…