# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

## Products of Michael spaces and completely metrizable spacesHTML articles powered by AMS MathViewer

by Dennis K. Burke and Roman Pol
Proc. Amer. Math. Soc. 129 (2001), 1535-1544 Request permission

## Abstract:

For disjoint subsets $A,C$ of $[0,1]$ the Michael space $M(A,C)=A\cup C$ has the topology obtained by isolating the points in $C$ and letting the points in $A$ retain the neighborhoods inherited from $[0,1]$. We study normality of the product of Michael spaces with complete metric spaces. There is a ZFC example of a LindelĂ¶f Michael space $M(A,C)$, of minimal weight $\aleph _1$, with $M(A,C)\times B(\aleph _0)$ LindelĂ¶f but with $M(A,C)\times B(\aleph _1)$ not normal. ($B(\aleph _\alpha )$ denotes the countable product of a discrete space of cardinality $\aleph _\alpha$.) If $M(A)$ denotes $M(A,[0,1]\smallsetminus A)$, the normality of $M(A)\times B(\aleph _0)$ implies the normality of $M(A)\times S$ for any complete metric space $S$ (of arbitrary weight). However, the statement â$M(A,C)\times B(\aleph _1)$ normal implies $M(A,C)\times B(\aleph _2)$ normalâ is axiom sensitive.
References
Similar Articles
• Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54E50, 54E52, 54D15
• Retrieve articles in all journals with MSC (1991): 54E50, 54E52, 54D15
• Dennis K. Burke
• Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
• Email: dburke@miavx1.muohio.edu
• Roman Pol
• Affiliation: Department of Mathematics, Warsaw University, Warsaw, Poland
• Email: pol@mimuw.edu.pl
• Received by editor(s): March 8, 1998
• Received by editor(s) in revised form: July 28, 1999
• Published electronically: October 10, 2000
• Additional Notes: The results in this note were obtained while the second author was a Visiting Professor at Miami University. The author would like to express his gratitude to the Department of Mathematics and Statistics of Miami University for their hospitality.
• Communicated by: Alan Dow