\begin{definition}[Definition: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'''.
\end{definition}