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

Author
V. K. Maslyuchenko, O. G. Fotiy
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.47.2.202-206
Reference
1. A. Rosenthal, On the continuity of functions of several variables, Math. Zeitschr., 63 (1955), 3138.

2. V. Maslyuchenko, . Fotiy On sequentially continuous functions, Bukovinian Math. Journal, 5 (2017) 1-2, 105111. (in Ukrainian)

3. Maslyuchenko V.K., Initial types of topological vector spaces, Chernivtsi: Ruta, 2002, 72 p. (in Ukrainian)

4. . Grauert, I. Lieb, V. Fischer, Differential and integral calculus, Moscow: Mir, 1971, 680 . (in Russian)

Pages
202-206
Volume
47
Issue
2
Year
2017
Journal
Matematychni Studii
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