Definition:Discrete Topology/Finite

Definition
Let $A \ne \varnothing$ be a set.

Let $\tau = \mathcal P \left({A}\right)$ be the power set of $A$.

If $A$ is finite, $\tau = \mathcal P \left({A}\right)$ is a finite discrete topology, and $\left({A, \tau}\right) = \left({A, \mathcal P \left({A}\right)}\right)$ is a finite discrete space.

Also see

 * Definition:Infinite Discrete Topology
 * Definition:Countable Discrete Topology
 * Definition:Uncountable Discrete Topology


 * Properties of Discrete Topology