Continuously differentiable curves detect limits of functions of two variables. (English)

Coll. Math. J. 45, No. 1, 54-56 (2014).

Summary: We present a result of Rosenthal, which shows that if a two-variable function has the same limit when evaluated over the graph of every convex function (in one variable or the other) with continuous first derivative, then the two-variable function is continuous. We give a new method of constructing the “testing curves” by using complex splines.