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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The $ {\rm SUP=MAX}$ problem for $ \delta$


Authors: Andrew J. Berner and István Juhász
Journal: Proc. Amer. Math. Soc. 99 (1987), 585-588
MSC: Primary 54A25
MathSciNet review: 875405
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Abstract: Let $ \delta \left( X \right) = \operatorname{sup}\{ d(D):D$ is a dense subspace of $ X\} $. It is shown that if $ \kappa $ is a limit cardinal, but not a strong limit, and $ {\text{cf}}\left( \kappa \right) > \omega $, then there is a 0-dimensional Hausdorff space $ X$ such that $ \delta \left( X \right) = \kappa $, but for all dense $ D \subset X,d(D) < \kappa $. For all other values of $ \kappa $, if $ X$ is Hausdorff and $ \delta \left( X \right) = \kappa $, then there is a dense $ D \subset X$ such that $ d\left( D \right) = \kappa $.


References [Enhancements On Off] (What's this?)

  • [1] István Juhász, Cardinal functions--Ten years later, Math. Centre Tract 123, Amsterdam, 1980.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0875405-9
PII: S 0002-9939(1987)0875405-9
Article copyright: © Copyright 1987 American Mathematical Society