Subset of Indiscrete Space is Compact and Sequentially Compact

Theorem

Let $T = \struct {S, \set {\O, S} }$ 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 $T$.