Products of Michael spaces and completely metrizable spaces

Authors:
Dennis K. Burke and Roman Pol

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1535-1544

MSC (1991):
Primary 54E50, 54E52, 54D15

DOI:
https://doi.org/10.1090/S0002-9939-00-05664-1

Published electronically:
October 10, 2000

MathSciNet review:
1712941

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Abstract | References | Similar Articles | Additional Information

Abstract: For disjoint subsets of the Michael space has the topology obtained by isolating the points in and letting the points in retain the neighborhoods inherited from . We study normality of the product of Michael spaces with complete metric spaces. There is a ZFC example of a Lindelöf Michael space , of minimal weight , with Lindelöf but with not normal. ( denotes the countable product of a discrete space of cardinality .) If denotes , the normality of implies the normality of for any complete metric space (of arbitrary weight). However, the statement `` normal implies normal'' is axiom sensitive.

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Additional Information

**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

DOI:
https://doi.org/10.1090/S0002-9939-00-05664-1

Keywords:
Michael space,
product spaces,
normal,
completely metrizable,
Baire space,
absolute $G_\delta$

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

Article copyright:
© Copyright 2000
American Mathematical Society