Some of the combinatorics

related to Michael's problem

Author:
J. Tatch Moore

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2459-2467

MSC (1991):
Primary 54D20, 54G15

DOI:
https://doi.org/10.1090/S0002-9939-99-04808-X

Published electronically:
April 8, 1999

MathSciNet review:
1486743

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present some new methods for constructing a Michael space, a regular Lindelöf space which has a non-Lindelöf 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:
https://doi.org/10.1090/S0002-9939-99-04808-X

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