Some ``almost-Dowker'' spaces

Author:
Brian M. Scott

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

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Abstract | References | Similar Articles | Additional Information

Abstract: Call *X* an AD-space (for ``almost-Dowker") if it is 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 , (e.g., if the continuum hypothesis holds), the ``Cantor tree of height '' is also such a space.

Since 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0467668-3

Keywords:
Dowker space,
orthocompact,
countably metacompact

Article copyright:
© Copyright 1978
American Mathematical Society