Let $f:I\to\mathbb{R}$ be a continuous function and $t_0\in I$ such that $f$ is analytic at $t_0$ and $f(t_0)=0$. Is it true that there is an entire neighbourhood of $t_0$ in which $f$ has no other zeros, excepting $t_0$?
2026-03-25 16:20:35.1774455635
Real analytic function in one point and zeros
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