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Products of R-factorizable groups. (English summary) Topology Proc. 39 (2012), 167–184. Summary: “We consider the Dieudonné and Hewitt-Nachbin completions, R-factorizability, and pseudo-ℵ1-compactness in products of spaces and topological groups in the case when one of the factors is a P-space. We prove that if X is a P-space and Y is a weakly Lindelöf space, then the formula µ(X × Y) = µX × µY holds. “We also show that the product G × K of a non-discrete R-factorizable P-group G with an R-factorizable group K is R-factorizable iff the space G × K is pseudo-ℵ1-compact. This theorem is complemented by the fact that the product of an R-factorizable P-group with a space Y is pseudo-ℵ1-compact provided that every locally countable family of open sets in Y is countable. As a corollary, we deduce that the product of an R-factorizable P-group with an R-factorizable weakly Lindelöf group is R-factorizable.” Reviewed by Oleg G. Okune

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MR2433295 (2010i, 22001

Year: 2000

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oai:CiteSeerX.psu:10.1.1.371.5617

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