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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Products with linear
and countable type factors


Authors: S. Purisch and M. E. Rudin
Journal: Proc. Amer. Math. Soc. 125 (1997), 1823-1830
MSC (1991): Primary 54D18, 54B10, 54D15, 54A25
MathSciNet review: 1415363
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Abstract: The basic theorem presented shows that the product of a linearly ordered space and a countable (regular) space is normal. We prove that the countable space can be replaced by any of a rather large class of countably tight spaces. Examples are given to prove that monotone normality cannot replace linearly ordered in the base theorem. However, it is shown that the product of a monotonically normal space and a monotonically normal countable space is normal.


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Additional Information

S. Purisch
Affiliation: Department of Mathematics, Barry University, Miami Shores, Florida 33161

M. E. Rudin
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04026-4
PII: S 0002-9939(97)04026-4
Keywords: Linearly ordered, countable, monotonically normal, product
Received by editor(s): August 14, 1995
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1997 American Mathematical Society