On functions that are continuous on differentiable curves (in Ukrainian) 

Author 
v.maslyuchenko@gmail.com; o.fotij@chnu.edu.ua
Chernivtsi National University, Chernivtsi, Ukraine

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 $x_0$.

Keywords 
normed space; continuity; differentiable curve

DOI 
doi:10.15330/ms.47.2.202206

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) 12, 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 
202206

Volume 
47

Issue 
2

Year 
2017

Journal 
Matematychni Studii

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