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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A local characterization of Darboux $ \mathcal{B}$ functions


Author: Richard G. Gibson
Journal: Proc. Amer. Math. Soc. 49 (1975), 505-509
MSC: Primary 54C10; Secondary 26A15
MathSciNet review: 0367899
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Abstract: A. M. Bruckner and J. B. Bruckner gave the definition of Darboux $ \mathcal{B}$ functions and proved a theorem which is a local characterization of real-valued Darboux $ \mathcal{B}$ functions. The purpose of this paper is to generalize this theorem. To this end, the definition of a function being Darboux $ \mathcal{B}$ at a point is given which has a metric continuum as its range. Hence, the theorem that a function is Darboux $ \mathcal{B}$ if and only if it is Darboux $ \mathcal{B}$ at each point.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0367899-4
PII: S 0002-9939(1975)0367899-4
Keywords: Darboux functions, Darboux $ \mathcal{B}$ functions, Darboux $ \mathcal{B}$ at a point, property $ {\text{L}}$
Article copyright: © Copyright 1975 American Mathematical Society