On Isbell's Density Theorem for bitopological pointfree spaces II

TL;DR

This paper extends Isbell's Density Theorem to bitopological pointfree spaces by characterizing extremal epimorphisms in biframes and analyzing the functorial properties of subbilocales.

Contribution

It introduces a pointfree analogue of Isbell's Density Theorem for bitopological spaces and studies the functoriality of subbilocales in biframes.

Findings

Existence of smallest dense subbiframe in biframes.

Characterization of extremal epimorphisms in biframes.

Functorial properties of subbilocales and their smallest dense subbilocales.

Abstract

With the aim of studying subspaces in pointfree bitopology, we characterize extremal epimorphism in biframes and show that a smallest dense one always exists, providing an analogue of Isbell's Density Theorem. Further we study the functoriality of assigning to each biframe its lattice of subbilocales and its smallest dense subbilocale.