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-frame SN σ Frm is equivalent to the category of separable strong Lindelöf nearness frames SepSLN-Frm. This then provides a structured version of the corresponding result on regular σ-frame and regular Lindelöf frames given by Madden and Vermeer in [13].