Discrete Space is Zero Dimensional/Proof 1

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $T = \struct {S, \tau}$ be a discrete space.

Then $T$ is zero dimensional.


Proof

We have from Partition of Singletons yields Discrete Topology that a discrete space is a partition space.

The result follows from Partition Topology is Zero Dimensional.

$\blacksquare$