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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Products of $\omega^*$ images


Authors: M. Bell, L. Shapiro and P. Simon
Journal: Proc. Amer. Math. Soc. 124 (1996), 1593-1599
MSC (1991): Primary 54D30, 06E05; Secondary 54B10, 54D40
MathSciNet review: 1328339
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Abstract: Let $\omega^*$ be the \u{C}ech-Stone remainder $\beta\omega \setminus \omega$. We show that there exists a large class $\cal O$ of images of $\omega^*$ such that whenever $\cal S$ is a subset of $\cal O$ of cardinality at most the continuum, then $\omega^* \times \prod {\cal S}$ is again an image of $\omega^*$. The class $\cal O$ contains all separable compact spaces, all compact spaces of weight at most $\omega_1$ and all perfectly normal compact spaces.


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Additional Information

M. Bell
Affiliation: Department of Mathematics, University of Manitoba, Fort Garry Campus, Winnipeg, Canada R3T 2N2
Email: mbell@cc.umanitoba.ca

L. Shapiro
Affiliation: Department of Mathematics, Academy of Labor and Social Relations, Lobachevskogo 90, Moscow, Russia 117454
Email: lshapiro@glas.apc.org

P. Simon
Affiliation: Matematick\a’y \a’Ustav, University Karlovy, Sokolovsk\a’a 83, 18600 Praha 8, Czech Republic
Email: psimon@ms.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03385-0
PII: S 0002-9939(96)03385-0
Keywords: $\omega^*$ image, product space, compact
Received by editor(s): October 20, 1994
Additional Notes: The first author gratefully acknowledges support from NSERC of Canada. The second author collaborated while visiting the University of Manitoba, Canada and also thanks the International Science Foundation for support. The third author gratefully acknowledges support by Charles University grant GAUK 350. We would like to thank A. Dow for helpful communications; in particular, for showing us his proof that $𝜔_{1} + 1$ is an orthogonal $𝜔^{*}$ image.
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1996 American Mathematical Society