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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…