Definition:Irrational Number Space
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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
- Results about the irrational number space can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $31$. The Irrational Numbers