Characterizations of Baire functions in general settings

Author:
Darwin E. Peek

Journal:
Proc. Amer. Math. Soc. **95** (1985), 577-580

MSC:
Primary 26A21; Secondary 54C30

DOI:
https://doi.org/10.1090/S0002-9939-1985-0810167-0

MathSciNet review:
810167

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Abstract | References | Similar Articles | Additional Information

Abstract: Baire* 1 functions from to were defined by R. J. O'Malley. For a general topological space , a function will be said to be Baire* 1 if and only if for every nonempty closed subset of , there is an open set such that and is continuous on . Several characterizations of Baire* 1 functions are found by altering the well-known Baire 1 characterization: If is a nonempty *closed subset* of the domain of , then has a point where is continuous. These conditions simply replace "*closed subset* of the preceding characterization with "*subset*", "*countable subset*" or "*dense-in-itself subset*". The relationships of these characterizations are examined with the domain of being various spaces. The independence of these conditions from the discrete convergence condition described by Á. Császár and M. Laczkovich is discussed.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0810167-0

Keywords:
Baire 1,
Baire* 1,
discrete convergence,
hereditarily separable

Article copyright:
© Copyright 1985
American Mathematical Society