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I vaguely remember that the real function defined as:

$$\forall x \in \mathbb R: f(x) = \begin{cases} 1 & : \text{$x$ is rational} \\ 0 & : \text {$x$ is irrational} \end{cases}$$

has a name attached to it, but I can't remember whose. Is it one of the Frenchmen whose names begin with L? I have a vague recollection but can't remember it.

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It is often referred to as Dirichlet function.

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It is called Dirichlet function.

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