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The Vietoris functor and modal operators on rings of continuous functions
G. Bezhanishvili, L. Carai, P. Morandi
We introduce an endofunctor on the category of bounded archimedean -algebras and show that there is a dual adjunction between the category of algebras for…
Free bounded archimedean -algebras
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We show that free objects on sets do not exist in the category of bounded archimedean -algebras. On the other hand, we introduce the category of weighted sets and prove…
Specker Algebras: A Survey
Guram Bezhanishvili, Patrick J. Morandi, Bruce Olberding
For a commutative ring with identity, a Specker -algebra is a commutative unital -algebra generated by a Boolean algebra of idempotents, each nonzero element of which is…
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…