On Lindelöf uniform frames and the axiom of countable choice

Abstract

This paper takes another look at the result that any complete separable uniform frame is Lindel¨of and some of its ramifications. In particular, it shows that this is equivalent to the axiom of countable choice and provides a new, considerably simpler proof of one of Shirota's original results on realcompactness.

Keywords:frame; regular Lindelöf; uniform frame; realcompact; complete

Quaestiones Mathematicae 30(2007), 115–121