Indiscrete Space is Hereditarily Compact

Theorem
Let $\left({S, \tau}\right)$ be an indiscrete topological space.

Then $\left({S, \tau}\right)$ is hereditarily compact.

Proof
Follows from Subset of Indiscrete Space is Compact and Sequentially Compact.

Also see

 * Hausdorff Space is Hereditarily Compact iff Finite