Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some ``almost-Dowker'' spaces

Author: Brian M. Scott
Journal: Proc. Amer. Math. Soc. 68 (1978), 359-364
MSC: Primary 54D15
MathSciNet review: 0467668
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D15

Retrieve articles in all journals with MSC: 54D15

Additional Information

Keywords: Dowker space, orthocompact, countably metacompact
Article copyright: © Copyright 1978 American Mathematical Society