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Heine Criterion

Last updated Nov 1, 2022

# Statement

Suppose $(X,d_{X})$, $(Y, d_{Y})$ are Metric Spaces. Suppose $f: X \to Y$ is a Function. Then $\lim\limits_{a \to x} f(a) = y$ If and Only If $f(x_{n}) \to y$ for all $({x}{n}){n=1}^{\infty} \subset X$.

# Proof

TODO