Aspects of nearness in σ-frames

Abstract

We introduce the notion of a nearness on a σ-frame. The concept of strong nearness for a σ-frame is intermediate between those of nearness and uniformity and we show that the category of strong nearness σ-frames SNσFrm is equivalent to the category of separable strong Lindeløf nearness frames SepSLNFrm. This then provides a structured version of the corresponding result on regular σ-frames and regular Lindelöf frames given by Madden and Vermeer in [13].

Keywords:σ-frame; nearness; uniform frame; Lindelöf; strong nearness; separable

Quaestiones Mathematicae 30(2007), 133–145