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On the representation of metric spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
A closure algebra is a set X with a closure operator C defined on it. It is possible to construct a topology τ on MX, the family of maximal, proper, closed subsets of X, and then to examine the relationship between the algebraic structure of (X, C) and the topological structure of the dual space (MX τ) This paper describes the algebraic conditions which are necessary and sufficient for the dual space to be separable metric and metric respectively.
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- Copyright © Australian Mathematical Society 1979
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