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Journal of the London Mathematical Society 1974 s2-8(2):339-344; doi:10.1112/jlms/s2-8.2.339
© 1974 by London Mathematical Society
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© Oxford University Press

An Example of Two Compact Hausdorff FrÉChet Spaces Whose Product is not Frechet

T. K. Boehme{dagger} and M Rosenfeld

University of California Santa Barbara, California 93106

A topological space such that each point in the closure of a subset A is the limit of a sequence in A is called a Fréchet space. It is shown that the product of a first countable space with a locally sequentially compact Fréchet space is Fréchet. It is shown using the continuum hypothesis that the product of two compact Hausdorff-Fréchet spaces need not be Fréchet. This answers a question posed by E. A. Michael in [7] and a question posed by J. D. Pryce in [8].

{dagger} This author was supported in part by NSF grant GP-34558.


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