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A Note On The Separability Of An Ordered Space

Published online by Cambridge University Press:  20 November 2018

B. J. Ball
B. J. Ball*
Affiliation:
University of Virginia
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An open interval of a simply ordered set S is a subset I of S such that either

(1) for some ,

(2) for some , or

(3) for some .

A simply ordered set with its interval topology (i.e., the topology in which “neighborhood of x” means “open interval containing x”) will be called an ordered space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 548 - 551
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Kurepa, G., La condition de Souslin et une propriété charaderistique des nombres réels, Comptes Rendus de L'Académie des Sciences (Paris), 231 (1950), 1113–1114.Google Scholar
2. Souslin, M., Problème 3, Fund. Math., 1 (1920), 223.Google Scholar