Some of the combinatorics related to Michael's problem
Author:
J. Tatch Moore
Journal:
Proc. Amer. Math. Soc. 127 (1999), 24592467
MSC (1991):
Primary 54D20, 54G15
Published electronically:
April 8, 1999
MathSciNet review:
1486743
Fulltext PDF Free Access
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Abstract: We present some new methods for constructing a Michael space, a regular Lindelöf space which has a nonLindelöf product with the space of irrationals. The central result is a combinatorial statement about the irrationals which is a necessary and sufficient condition for the existence of a certain class of Michael spaces. We also show that there are Michael spaces assuming and that it is consistent with that there is a Michael space. The influence of Cohen reals on Michael's problem is discussed as well. Finally, we present an example of a Michael space of weight less than under the assumption that (whose product with the irrationals is necessarily linearly Lindelöf).
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Additional Information
J. Tatch Moore
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
Email:
justin@math.toronto.edu
DOI:
http://dx.doi.org/10.1090/S000299399904808X
PII:
S 00029939(99)04808X
Keywords:
Lindel\"of,
linearly Lindel\"of,
irrationals,
Michael space.
Received by editor(s):
September 22, 1997
Received by editor(s) in revised form:
October 29, 1997
Published electronically:
April 8, 1999
Communicated by:
Alan Dow
Article copyright:
© Copyright 1999
American Mathematical Society
