Mathematics Commons^™

A Continuous Tale On Continuous And Separately Continuous Functions, Krzysztof Ciesielski

Faculty & Staff Scholarship

Assume that you have developed a good set of tools allowing you to decide which real functions of one real variable, f : R → R, are continuous. (Q): How can such a tool-box be utilized to decide on the continuity of the functions g : R n → R of n real variables? This is one of the questions which must be faced by any student taking multivariable calculus. Of course, such a student is following the footsteps of many generations of mathematicians, which were, and still are, struggling with the same general question. The aim of this article …