On the Strict Completion of a Nearness Space

The strict completion of a nearness space was constructed in 1974 in Herrlich's original paper on nearness. we present an external characterization of this completion. Among the consequences of this result is the fact that for nearness spaces X and Y with completions X* and Y*, if X ⊂ Y ⊂ X* then Y* is isomorphic to X*.Mathematics Subject Classification (1991): 54E17, 54D35, 54E15 Keywords: completeness, nearness space, completion, initial map, strict map, dense map, nearness spaces, extensions of spaces, uniform structures and generalizations, completions Quaestiones Mathematicae 24(1) 2001, 39–5