Definition:Indiscrete Topology

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

Let $\tau = \left\{{S, \varnothing}\right\}$.

Then $\tau$ is called the indiscrete topology on $S$.

A topological space $\left({S, \left\{{S, \varnothing}\right\}}\right)$ is known as an indiscrete space.

Also known as

 * The trivial topology (on $S$)
 * The nondiscrete topology (on $S$)

Also see

 * Indiscrete Topology is Topology
 * Indiscrete Topology is Coarsest Topology