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

Evans M. J., Humke P. D.

Journal of Applied Analysis

2010

Vol. 16, nr 1

135-149

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.