Properties of Discrete Topology

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

$\forall U \subseteq S: U$ is both closed and open in $\struct {S, \tau}$.

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 $T$.