# Properties of Discrete Topology

## Properties of Discrete Topology

Let $T = \left({S, \tau}\right)$ be a discrete topological space.

This page gathers up some results about $\left({S, \tau}\right)$.

### Discrete Topology is Topology

$\tau$ is a topology on $S$.

### Set in Discrete Topology is Clopen

$\forall U \subseteq S: U$ is both closed and open in $\left({S, \tau}\right)$.

### Discrete Topology is Finest Topology

$\tau$ is the finest topology on $S$.