Original Articles

ON THE STRICT COMPLETION OF A NEARNESS SPACE

Published in: Quaestiones Mathematicae
Volume 24 , issue 1 , 2001 , pages: 39–50

DOI: 10.1080/16073606.2001.9639771

Author(s): H.L. Bentley , USA , H. Herrlich , Germany

Keywords: 54E17 , 54D35 , 54E15 , 54E17 , 54D35 , 54E15

Abstract

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*.

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