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Products of images
Authors:M. Bell   L. Shapiro   P. Simon
Affiliation:Department of Mathematics, University of Manitoba, Fort Garry Campus, Winnipeg, Canada R3T 2N2 ; Department of Mathematics, Academy of Labor and Social Relations, Lobachevskogo 90, Moscow, Russia 117454 ; Matematický Ústav, University Karlovy, Sokolovská 83, 18600 Praha 8, Czech Republic
Abstract:Let $omega^*$ be the u{C}ech-Stone remainder $betaomega setminus omega$. 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.

Keywords:$omega^*$ image   product space   compact
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