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Continuously Differentiable Curves Detect Limits of Functions of Two Variables

Ollie Nanyes
The College Mathematics Journal
Vol. 45, No. 1 (January 2014), pp. 54-56
DOI: 10.4169/college.math.j.45.1.054
Stable URL: http://www.jstor.org/stable/10.4169/college.math.j.45.1.054
Page Count: 3
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Continuously Differentiable Curves Detect Limits of Functions of Two Variables
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Abstract

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.

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