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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Baire functions and their restrictions to special sets


Author: Darwin E. Peek
Journal: Proc. Amer. Math. Soc. 30 (1971), 303-307
MSC: Primary 26.35
MathSciNet review: 0285676
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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\vert H$ contains a point where $ f\vert 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.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0285676-6
Keywords: Baire class 1, Baire functions, perfect spaces, pointwise convergence, totally imperfect sets, uniform convergence
Article copyright: © Copyright 1971 American Mathematical Society