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Two remarks on A. Gleason's factorization theorem

1970
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Bulletin of the American Mathematical Society
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The theorem of A. Gleason [2, vii.23] asserts that every continuous map ƒ from an open subset U of a product X of separable topological spaces into a Hausdorff space Y whose points are Gs-sets has the form goir\uy where ir is a countable projection of X and g: ir(U)-> Y is continuous. A natural question is to find what other "pleasant" subsets U of X have the above factorization property. The most plausible ones are compact subsets: for, if UQX is compact and f = goTr\u with ƒ continuous, then

doi:10.1090/s0002-9904-1970-12482-x
fatcat:ibbgtyjukfhnpbnxrxahgzc7ju