Paper read at the Second Symposium on Categorical Topology at the University of Cape Town 9–13 August 1976

A NOTION OF COMPLETENESS OF TOPOLOGICAL STRUCTURES

Published in: Quaestiones Mathematicae
Volume 2 , issue 1-3 , 1977 , pages: 235–243

DOI: 10.1080/16073606.1977.9632545

Author(s): Kazumi Nakano Department of Mathematics, U.S.A.

Keywords: primary 54A05 , 54D30 , 54E15 , secondary 18B99 , 54C05 , 54C25 , 54C60 , primary 54A05 , 54D30 , 54E15 , secondary 18B99 , 54C05 , 54C25 , 54C60

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Abstract

A connector U on a space S is a function from S to the power set of S such that each x in s belongs to its image. The image of x is denoted by xU. In other words, the relation {(x,y): y ϵ xU, x ϵ S) is a reflexive binary relation. A space with a certain set of connectors is a generalization of topological spaces as well as uniform spaces. In this paper, a notion of completeness of such a space is introduced. This completeness corresponds to completeness of uniform spaces if a set of cannectors meets the conditions of uniformity. Compactness of topological Spaces is a special case of the completeness.

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