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It is well known that if two continuous functions, both $\mathbb{R} \rightarrow \mathbb{R}$, agree on the rationals then they are equal. Indeed, a more general result involving dense subsets and Hausdorff spaces is true.

Does this result have a name? If not, is there a standard or obvious way to refer to it?

J. W. Tanner
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Jamie Ballingall
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    I don't think it has a name. The result says that a continuous function is uniquely determined by its values on a dense subset. In other words, a function defined on a dense subset has at most one continuous extension. – Jakobian Jan 15 '24 at 02:08

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