# Subset of Indiscrete Space is Compact and Sequentially Compact

## Theorem

Let $T = \left({S, \left\{{\varnothing, S}\right\}}\right)$ be an indiscrete topological space.

Let $H \subseteq S$.

### Subset of Indiscrete Space is Compact

$H$ is compact in $T$.

### Subset of Indiscrete Space is Sequentially Compact

$H$ is sequentially compact in $T$.