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An Example of Two Compact Hausdorff FrÉChet Spaces Whose Product is not Frechet
Author(s) -
Boehme T. K.,
Rosenfeld M
Publication year - 1974
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-8.2.339
Subject(s) - hausdorff space , mathematics , urysohn and completely hausdorff spaces , product (mathematics) , limit of a sequence , fréchet space , product topology , closure (psychology) , pure mathematics , space (punctuation) , countable set , locally compact space , second countable space , topological space , normal space , limit (mathematics) , sequence (biology) , mathematical analysis , topological vector space , interpolation space , hausdorff measure , geometry , functional analysis , hausdorff dimension , computer science , chemistry , biochemistry , gene , genetics , biology , operating system , market economy , economics
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 ].
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