Products of Michael spaces and completely metrizable spaces
Authors:
Dennis K. Burke and Roman Pol
Journal:
Proc. Amer. Math. Soc. 129 (2001), 15351544
MSC (1991):
Primary 54E50, 54E52, 54D15
Published electronically:
October 10, 2000
MathSciNet review:
1712941
Fulltext PDF Free Access
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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:
http://dx.doi.org/10.1090/S0002993900056641
PII:
S 00029939(00)056641
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
