On the continuity and differentiability of functions along regular curves (Q1065182)
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scientific article; zbMATH DE number 3920841
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the continuity and differentiability of functions along regular curves |
scientific article; zbMATH DE number 3920841 |
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On the continuity and differentiability of functions along regular curves (English)
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1985
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The main result of the paper is the following theorem: If a function defined on the d-dimensional Euclidean space is continuous at some point p along every regular (i.e. with non-vanishing derivative) curve, then it is continuous at p. The above theorem is used to prove Fréchet differentiability of a function assuming differentiability along regular curves.
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Fréchet differentiability
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differentiability along regular curves
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