arXiv subjects

Ranjitha Raviprakash

Publications and source records attributed to Ranjitha Raviprakash.

5 recordsLinked to original sources

arXiv2026

A choice-free approach to Wallman compactifications

The classical Wallman compactification of a $T_1$-space and the Stone--Čech compactification of a completely regular space rely on choice principles. We show that, by representing a space by its powerset MT-algebra (McKinsey--Tarski algebra), both constructions admit choice-free compactifications. More generally, from any Wallman basis of a spatial $T_1$ MT-algebra we construct a compact $T_1$ MT-algebra which is a compactification of the original algebra. Taking the basis of all closed elements yields a choice-free Wallman compactification of every spatial $T_1$ MT-algebra, while taking the basis of zero-elements yields a choice-free Stone--Čech compactification of every spatial completely regular MT-algebra. Choice is only needed to show that the resulting compactifying algebras are spatial, and hence to recover the usual compactifying spaces. We also show that these constructions recover the corresponding compactifications of frames of opens.

math.GN↗

arXiv2026

McKinsey-Tarski algebras and Raney extensions

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 the construction of the Funayama envelope of a frame. The resulting notion of the $T_0$-hull of a Raney extension generalizes that of the $T_D$-hull of a frame.

math.CT↗

arXiv2025

The Funayama envelope as the $T_D$-hull of a frame

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 of a frame, which is viewed as the $T_D$-hull. Our results have some spatial ramifications, including a generalization of the $T_D$-duality of Banaschewski and Pultr.

math.CT↗

arXiv2024

Local compactness in MT-algebras

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-algebras. We establish the Hofmann-Mislove theorem for sober MT-algebras, using which we develop the MT-algebra versions of such well-known dualities in pointfree topology as Hofmann-Lawson, Isbell, and Stone dualities. This yields a new perspective on these classic results.

math.GN↗

arXiv2023

McKinsey-Tarski Algebras: An alternative pointfree approach to topology

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 McKinsey-Tarski algebras or simply MT-algebras. Associating with each MT-algebra the lattice of its open elements defines a functor from the category of MT-algebras to the category of frames, which we study in depth. We also study the dual adjunction between the categories of MT-algebras and topological spaces, and show that MT-algebras provide a faithful generalization of topological spaces. Our main emphasis is on developing a unified approach to separation axioms in the language of MT-algebras, which generalizes separation axioms for both topological spaces and frames.

math.GN↗