
06495907
j
2015f.00833
Nanyes, Ollie
Continuously differentiable curves detect limits of functions of two variables.
Coll. Math. J. 45, No. 1, 5456 (2014).
2014
Mathematical Association of America (MAA), Washington, D.C.
EN
I65
I55
twovariable functions
continuous differentiable curves
splines
doi:10.4169/college.math.j.45.1.054
Summary: We present a result of Rosenthal, which shows that if a twovariable 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 twovariable function is continuous. We give a new method of constructing the ``testing curves'' by using complex splines.