Separately continuous functions on Rn: from Cauchy mistake, through Lebesgue contributions, to contemporary results


Krzysztof Chris Ciesielski,

unpublished notes of 2012.

We will briefly describe a history of study of functions from Rn to R that are continuous with respect to each variable or, more generally, when restricted to different surfaces of co-dimension 1. In particular, we present a new elementary example of a discontinuous function of n-variables whose restriction to any hyperplane is continuous.

Full text on line in pdf format.

Last modified June 17, 2012.