One-to one Carathéodory representation theorem for multifunctions with uncountable values
A. Ioffe (1980)
Fundamenta Mathematicae
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Displaying similar documents to “Functionally Countable Spaces and Baire Functions”
One-to one Carathéodory representation theorem for multifunctions with uncountable values
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Bulletin of the Polish Academy of Sciences. Mathematics
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We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".
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It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.
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J. Bourgain (1979)
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Šmídek, M. (1995)
Acta Mathematica Universitatis Comenianae. New Series
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