Czechoslovak Mathematical Journal

, Volume 60, Issue 2, pp 549–569 | Cite as

Two classes of Darboux-like, Baire one functions of two variables

  • Michael J. Evans
  • Paul D. Humke


Among the many characterizations of the class of Baire one, Darboux realvalued functions of one real variable, the 1907 characterization of Young and the 1997 characterization of Agronsky, Ceder, and Pearson are particularly intriguing in that they yield interesting classes of functions when interpreted in the two-variable setting. We examine the relationship between these two subclasses of the real-valued Baire one defined on the unit square.

MSC 2010

26B05 26A21 


Woodcutters Problem Baire one Darboux 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. J. Agronsky, J. G. Ceder, T. L. Pearson: Some characterizations of Darboux Baire 1 functions. Real Anal. Exch. 23 (1997), 421–430.MATHMathSciNetGoogle Scholar
  2. [2]
    A. M. Bruckner: Differentiation of Real Functions. CRM Monograph Series, Vol. 5. American Mathematical Society (AMS), 1994.Google Scholar
  3. [3]
    A. S. Cavaretta, W. Dahmen, C. A. Micchelli: Stationary Subdivision. Mem. Am. Math. Soc. 453 (1991).Google Scholar
  4. [4]
    M. J. Evans and P. D. Humke: A characterization of Baire one functions of two variables. J. Math. Anal. Appl. 335 (2007), 1–6.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    M. J. Evans and P. D. Humke: Revisiting a century-old characterization of Baire class one, Darboux functions. Am. Math. Mon. 116 (2009), 451–455.CrossRefMathSciNetGoogle Scholar
  6. [6]
    M. J. Evans and P. D. Humke: Collections of Darboux-like, Baire one functions of two variables. To appear in J. Appl. Anal.Google Scholar
  7. [7]
    K. Kuratowski: Topology, Vol. I. Academic Press, New York, 1966.Google Scholar
  8. [8]
    J. Malý: The Darboux property for gradients. Real Anal. Exch. 22 (1996), 167–173.MATHGoogle Scholar
  9. [9]
    C. A. Micchelli and H. Prautzsch: Uniform refinement of curves. Linear Algebra Appl. 114/115 (1989), 841–870.CrossRefMathSciNetGoogle Scholar
  10. [10]
    W. H. Young: A theorem in the theory of functions of a real variable. Rend. Circ. Mat. Palermo 24 (1907), 187–192.MATHCrossRefGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2010

Authors and Affiliations

  1. 1.Washington and Lee UniversityLexingtonUSA
  2. 2.St. Olaf CollegeNorthfieldUSA

Personalised recommendations