Quasi-nearness biframes: unique completions and related covering properties

Abstract

Quasi-completeness was considered in [16], where a quasi-completion was constructed for any quasi-nearness biframe. In this paper, we compare the familiar notions of compactness and total boundedness with quasi-completeness. We investigate the uniqueness of quasi-completions, using the full and balanced biframes of [17]. In the case of quasi-uniform biframes it makes sense to compare this quasi-completion with the completion of [13] and [14] – surprisingly, they need not coincide.