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Discussion on question by questmath: $\lim_{x \to \infty} f(x)=1$ and $\lim_{x \to -\infty}f(x)=-1$ and the function is not uniformly continuous

Imported from a comment discussion on math.stackexchange.com/questions/4065520/…

functional-analysis uniform-continuity

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Discussion on question by questmath: $\lim_{x \to \infty} f(x)=1$ and $\lim_{x \to -\infty}f(x)=-1$ and the function is not uniformly continuous