6 papers
A choice-free approach to Wallman compactifications
Sebastian D Melzer, Cerene Rathilal, Ranjitha Raviprakash
The classical Wallman compactification of a -space and the Stone--Čech compactification of a completely regular space rely on choice principles. We show that, by representing…
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…
Local compactness does not always imply spatiality
G. Bezhanishvili, S. D. Melzer, R. Raviprakash +1
It is a well-known result in pointfree topology that every locally compact frame is spatial. Whether this result extends to MT-algebras (McKinsey-Tarski algebras) was an open probl…
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…
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…
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…