# Properties of Discrete Topology

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## Properties of Discrete Topology

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

This page gathers up some results about $\struct {S, \tau}$.

### Set in Discrete Topology is Clopen

### Discrete Topology is Finest Topology

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

### Topological Space is Discrete iff All Points are Isolated

- $\tau$ is the discrete topology on $S$ if and only if all points in $S$ are isolated points of $T$.