Definition:Discrete Topology/Uncountable

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

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

If $A$ is uncountably infinite, $\tau = \mathcal P \left({A}\right)$ is an uncountable discrete topology, and $\left({A, \tau}\right) = \left({A, \mathcal P \left({A}\right)}\right)$ is an uncountable discrete space.

Also see

 * Definition:Finite Discrete Topology


 * Definition:Countable Discrete Topology


 * Properties of Discrete Topology