# Category:Irrational Number Space

Let $\mathbb I := \R \setminus \Q$ be the set of irrational numbers.
Let $d: \mathbb I \times \mathbb I \to \R$ be the Euclidean metric on $\mathbb I$.
Let $\tau_d$ be the topology on $\mathbb I$ induced by $d$.
Then $\struct {\mathbb I, \tau_d}$ is the irrational number space.