Rational Number Space is Separable

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Theorem

Let $\struct {\Q, \tau_d}$ be the rational number space under the Euclidean topology $\tau_d$.


Then $\struct {\Q, \tau_d}$ is separable.


Proof

From Rational Numbers are Countably Infinite, $\Q$ is itself countable.

The result follows by Countable Space is Separable.

$\blacksquare$


Sources