Definition:Irrational Number Space

Definition
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.

Also see

 * Irrational Number Space is Topological Space