Let $\{f_n \}$ is equicontinuous and pointwise converge to $f$ now is $f$ uniformly continuous ? I can prove f is continuous but is this uniformly continuous? and we know every $f_n$ is uniformly continuous. Is $ f_n$ uniformly convergent to $f$ ? prove or disprove.
2026-03-29 11:44:30.1774784670
$\{f_n \}$ is equicontinuous and pointwise converge to f is f uniformly continuous?
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Take any $f$ that is not uniformly continuous.
Let $f_n = f+{1 \over n}$.
Then the $f_n$ are equicontinuous and converge pointwise to $f$ which is not uniformly continuous