Collections of Darboux-like, Baire one functions of two variables

• Autorzy: Evans M. J. , Humke P. D.
• Języki publikacji: EN

Abstrakty

EN

The collection of Baire class one, Darboux functions from [0,1] to R is a rich class of functions that has been intensely investigated and characterized over the years. Which Baire class one, real-valued functions defined on [0,1] x [0,1] form the most "natural" extension of this class to the two-variable setting is debatable, with many suggestions having been advanced. In light of recent interest in Darboux-like properties for derivatives (i.e. gradients) of differentiable functions of two variables, it seems that now is a good time to consider some of the most feasible notions of "Darboux-like" and investigate the relationships between them.

Słowa kluczowe

EN

Baire one; Darboux; connected

PL

Baire 1; Darboux; spójny

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2010
• Tom: Vol. 16, nr 1
• Strony: 135--149
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Evans M. J.

autor

Humke P. D.

• Department of Mathematics, Washington and Lee University, Lexington, VA 24450, USA.,

Bibliografia

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• [4] A. M. Bruckner and J. B. Bruckner, Darboux transformations, Trans. Amer. Math. Soc. 128(1967), 103-111.
• [5] J. Ceder, Two-dimensional Darboux functions, Rev. Roum. Math. Pures Appl. 28 (1983), 795-802. .
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• [7] M. J. Evans and P. D. Humke, A characterization of Baire one functions of two variables, J. Math. Anal. Appl. 335 (2007), 1-6.
• [8] M. J. Evans and P. D. Humke, Revisiting a century-old characterization of Baire class one, Darboux functions, Amer. Math. Monthly 116 (2009), 451-455.
• [9] M. J. Evans and P. D. Humke, Two classes of Darboux-like, Baire one functions of two variables, Czech. Math. J. 60 (135) (2010), 549-569.
• [10] R. Gibson and T. Natkaniec, Darboux like functions, Real Anal. Exch. 22 (1996-1997), 492-533.
• [11] J. Malý, The Darboux property for gradients. Real Anal. Exch. 22 (1996-1997), 167-173.
• [12] L. Mišik, Über die Funktionen der ersten Baireschen Klasse mit der Eigenschaft van Darboux, Mat. Fyz. Casopis Sloven. Akad. Vied 14 (1964), 44-49.
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• [15] W. H. Young, A theorem in the theory of functions of a real variable, Rend. Circ. Mat. Palermo 24 (1907), 187-192.