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On the Strict Completion of a Nearness Space
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*.
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, 39–50
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, 39–50
