Almost new pre-apartness from old

Continuing the constructive theory of pre-apartness on frames, we investigate, in the context of an a-frame L and its product P with itself, a subset Bw of P whose counterpart in the context of a uniform space and the related apartness is closely linked with total boundedness. We also discuss the connection between the given pre-apartness on L and a certain binary relation associated with Bw, also analogous to a binary relation on subsets of a uniform space.