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The normality in products with a countably compact factor |
Published:1998-06-01
Printed: Jun 1998
Printed: Jun 1998
- Lecheng Yang
Abstract
It is known that the product $\omega_1 \times X$ of
$\omega_1$ with an $M_1$-space may be nonnormal. In this paper we
prove that the product $\kappa \times X$ of an uncountable regular
cardinal $\kappa$ with a paracompact semi-stratifiable space is normal
if{f} it is countably paracompact. We also give a sufficient
condition under which the product of a normal space with a paracompact
space is normal, from which many theorems involving such a product
with a countably compact factor can be derived.
| MSC Classifications: |
54B19 - unknown classification 54B19 54D15 - Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54D20 - Noncompact covering properties (paracompact, Lindelof, etc.) |