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 $x_0\in X,$ and a mapping $f\colon X\to Y$, the continuity of all compositions $f\circ \omega\colon [0,1]\to Y$ at zero on differentiable curves $\omega\colon [0,1]\to X$ with $\omega(0)=x_0$ yields the continuity of $f$ at $x_0$.
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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, Î. 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. Í. Grauert, I. Lieb, V. Fischer, Differential and integral calculus, Moscow: Mir, 1971, 680 ð. (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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