The $\textrm {SUP=MAX}$ problem for $\delta$
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- by Andrew J. Berner and István Juhász PDF
- Proc. Amer. Math. Soc. 99 (1987), 585-588 Request permission
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
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István Juhász, Cardinal functions—Ten years later, Math. Centre Tract 123, Amsterdam, 1980.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 585-588
- MSC: Primary 54A25
- DOI: https://doi.org/10.1090/S0002-9939-1987-0875405-9
- MathSciNet review: 875405