Lebesgue sets and insertion of a continuous function

Author:
Ernest P. Lane

Journal:
Proc. Amer. Math. Soc. **87** (1983), 539-542

MSC:
Primary 54C05; Secondary 54C30

DOI:
https://doi.org/10.1090/S0002-9939-1983-0684654-0

MathSciNet review:
684654

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Abstract: Necessary and sufficient conditions in terms of Lebesgue sets are presented for the following two insertion properties for real-valued functions defined on a topological space: (1) there is a continuous function such that , and for each for which then . (2) there is a continuous function such that .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0684654-0

Keywords:
Insertion of continuous functions,
Lebesgue set,
completely separated

Article copyright:
© Copyright 1983
American Mathematical Society