Baire functions and their restrictions to special sets
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- by Darwin E. Peek PDF
- Proc. Amer. Math. Soc. 30 (1971), 303-307 Request permission
Abstract:
A function f from a complete and separable metric space X into the real numbers is of Baire class 1 iff for every nonempty perfect subset H of X, $f|H$ contains a point where $f|H$ is continuous. This paper examines a similar idea obtained by changing “perfect subset H” to “union of a countable collection of perfect subsets” in the preceding characterization of Baire class 1 functions. This new idea is also characterized by using “condensation points” and “totally imperfect sets.” Functions of this new type are of Baire class 1. However, the converse is false.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 303-307
- MSC: Primary 26.35
- DOI: https://doi.org/10.1090/S0002-9939-1971-0285676-6
- MathSciNet review: 0285676