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On the representation of metric spaces

Published online by Cambridge University Press:  17 April 2009

G.J. Logan
G.J. Logan
Affiliation:
Department of Applied Sciences, Christchurch Technical Institute, Christchurch, New Zealand.
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Abstract

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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 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 3 , June 1979 , pp. 367 - 375
Copyright
Copyright © Australian Mathematical Society 1979

References

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