Sorgenfrey Line is Separable

Theorem

The Sorgenfrey line is separable.

Proof

By Rationals are Everywhere Dense in Sorgenfrey Line:

$\Q$ is dense in the Sorgenfrey line.

By Rational Numbers are Countably Infinite:

$\Q$ is countable.

Thus by definition:

The Sorgenfrey line is separable.

$\blacksquare$

Sources

• 1989: Ryszard Engelking: General Topology (revised and completed ed.)

• Mizar article TOPGEN_5:44