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Continuously Differentiable Curves Detect Limits of Functions of Two Variables

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Abstract:

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.

Document Type: Research Article

DOI: http://dx.doi.org/10.4169/college.math.j.45.1.054

Publication date: January 1, 2014

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maa/cmj/2014/00000045/00000001/art00014
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