Definition:Discrete Topology/Countable

Definition
Let $A \ne \varnothing$ be an infinite set.

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

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

Also see

 * Definition:Finite Discrete Topology
 * Definition:Infinite Discrete Topology


 * Definition:Uncountable Discrete Topology


 * Properties of Discrete Topology