On functions that are continuous on differentiable curves (in Ukrainian)
Chernivtsi National University, Chernivtsi, Ukraine
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 $x_0$.
normed space; continuity; differentiable curve
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