Rational Numbers are not Discrete Space

Theorem

The set of rational numbers $\Q$ does not form a discrete space.

Proof

Follows from:

Rational Number Space is not Extremally Disconnected

Discrete Space is Extremally Disconnected.

$\blacksquare$

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $6.5$: Components: Examples $6.5.1$