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Some of the combinatorics related to Michael's problem |
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| Authors: | J. Tatch Moore |
| Affiliation: | Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1 |
| 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). |
| Keywords: | Lindel" of, linearly Lindel" of, irrationals, Michael space. |
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