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On the representation of metric spaces

1979
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Bulletin of the Australian Mathematical Society
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A closure algebra is a set X with a closure operator C defined on it. It is possible to construct a topology x on M v , the family of maximal, proper, closed subsets of I , and then to examine the relationship between the algebraic structure of {X, C) and the topological structure of the dual space [My, x) . This paper describes the algebraic conditions which are necessary and sufficient for the dual space to be separable metric and metric respectively. In Logan [3] a method was given for

doi:10.1017/s0004972700011072
fatcat:kmmetlglkvfi3kbw3l52wmn36q