Some “almost-Dowker” spaces
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- by Brian M. Scott PDF
- Proc. Amer. Math. Soc. 68 (1978), 359-364 Request permission
Abstract:
Call X an AD-space (for “almost-Dowker") if it is ${T_3}$ but not countably metacompact. We construct, without set-theoretic assumptions, a class of zero-dimensional, orthocompact, nonnormal AD-spaces. Using the same techniques, we simplify an example due to Hayashi by showing that if $\exp (\exp (\omega )) = \exp ({\omega _1})$, (e.g., if the continuum hypothesis holds), the “Cantor tree of height ${\omega _1}$” is also such a space. Since $X \times [0,1]$ is orthocompact iff X is orthocompact and countably metacompact, we now have “absolute” examples of orthocompact Tikhonov spaces whose products with [0, 1] are not orthocompact.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 359-364
- MSC: Primary 54D15
- DOI: https://doi.org/10.1090/S0002-9939-1978-0467668-3
- MathSciNet review: 0467668