A local characterization of Darboux $\mathcal {B}$ functions
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- by Richard G. Gibson PDF
- Proc. Amer. Math. Soc. 49 (1975), 505-509 Request permission
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.References
- A. M. Bruckner and J. B. Bruckner, Darboux transformations, Trans. Amer. Math. Soc. 128 (1967), 103–111. MR 218500, DOI 10.1090/S0002-9947-1967-0218500-1
- A. M. Bruckner and J. G. Ceder, Darboux continuity, Jber. Deutsch. Math.-Verein. 67 (1964/65), no. Abt. 1, 93–117. MR 186761
- James Dugundji, Topology, Allyn and Bacon Series in Advanced Mathematics, Allyn and Bacon, Inc., Boston, Mass.-London-Sydney, 1978. Reprinting of the 1966 original. MR 0478089
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 505-509
- MSC: Primary 54C10; Secondary 26A15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0367899-4
- MathSciNet review: 0367899