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.)
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