On functions that are continuous on differentiable curves (in Ukrainian) |
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| Author |
v.maslyuchenko@gmail.com; o.fotij@chnu.edu.ua
Chernivtsi National University, Chernivtsi, Ukraine
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| Abstract |
We prove that for a normed space X, a topological space Y, a point x0∈X, and a mapping f:X→Y, the continuity of all compositions f∘ω:[0,1]→Y at zero on differentiable curves ω:[0,1]→X with ω(0)=x0 yields the continuity of f at x0.
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| Keywords |
normed space; continuity; differentiable curve
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| DOI |
doi:10.15330/ms.47.2.202-206
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| Reference |
1. A. Rosenthal, On the continuity of functions of several variables, Math. Zeitschr., 63 (1955), 31–38.
2. V. Maslyuchenko, О. Fotiy On sequentially continuous functions, Bukovinian Math. Journal, 5 (2017) 1-2, 105–111. (in Ukrainian) 3. Maslyuchenko V.K., Initial types of topological vector spaces, Chernivtsi: Ruta, 2002, 72 p. (in Ukrainian) 4. Н. Grauert, I. Lieb, V. Fischer, Differential and integral calculus, Moscow: Mir, 1971, 680 р. (in Russian) |
| Pages |
202-206
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| Volume |
47
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| Issue |
2
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| Year |
2017
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| Journal |
Matematychni Studii
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