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Hewitt Realcompactifications of Products

Published online by Cambridge University Press:  20 November 2018

William G. McArthur
William G. McArthur*
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania Shippensburg State Collège, Shippensburg, Pennsylvania
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The Hewitt realcompactification vX of a completely regular Hausdorff space X has been widely investigated since its introduction by Hewitt [17]. An important open question in the theory concerns when the equality v(X × Y) = vX × vY is valid. Glicksberg [10] settled the analogous question in the parallel theory of Stone-Čech compactifications: for infinite spaces X and Y, β(X × Y) = βX × β Y if and only if the product X × Y is pseudocompact. Work of others, notably Comfort [3; 4] and Hager [13], makes it seem likely that Glicksberg's theorem has no equally specific analogue for v(X × Y) = vX × vY. In the absence of such a general result, particular instances may tend to be attacked by ad hoc techniques resulting in much duplication of effort.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 3 , 01 June 1970 , pp. 645 - 656
Copyright
Copyright © Canadian Mathematical Society 1970

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