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A characterization of frontier

Published online by Cambridge University Press:  24 October 2008

K. A. H. Gravett  and
D. B. Scott
K. A. H. Gravett
Affiliation:
Balliol CollegeOxford
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Extract

Let X be a set and let f be a mapping of P(X), the set of all subsets of X, into P(X). Conditions are given which are necessary and sufficient for there to exist a topology on the set X with respect to which, for all S ∈ P(X), the frontier of S is fS.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 1 , January 1956 , pp. 152 - 153
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

* It is not difficult to show that no four of the properties I–V entails the remaining property.