Definition:Rational Number Space

Definition

Let $\Q$ be the set of rational numbers.

Let $d: \Q \times \Q \to \R$ be the Euclidean metric on $\Q$.

Let $\tau_d$ be the topology on $\Q$ induced by $d$.

Then $\struct {\Q, \tau_d}$ is the rational number space.

Also see

• Rational Number Space is Topological Space

• Results about the rational 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: $30$. The Rational Numbers