Quasi-nearnesses on biframes and their completions

Abstract

We introduce quasi-nearness biframes. They provide a generalization of both nearness frames [5] and quasi-uniform biframes [12]. Quasi-nearness biframes are regular; they are normal if and only if the standard binary quasi-nearness is in fact a quasi-uniformity. Further, we introduce a notion of completeness, and provide a construction of a completion in which we make use of the new notion of a part-preserving right adjoint of a biframe map.