Properties of Discrete Topology

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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 $S$.