Bi-Alexandroff spaces

Abstract

Bi-Alexandroff spaces are defined as extensions of Alexandroff spaces [1]. Urysohn's lemma for bi-Alexandroff spaces is used to show that upper and lower cozero sets of bitopological spaces are bi-Alexandroff spaces. An adjunction between bi-Alexandroff spaces and pairwise completely regular bitopological spaces is established.

Keywords: Bi-Alexandroff spaces, bitopological spaces, upper and lower cozero sets

Quaestiones Mathematicae 30(2007), 57–65