# Totally Disconnected Space is Punctiform

## Theorem

Let $T = \left({S, \tau}\right)$ be a topological space which is totally disconnected.

Then $T$ is punctiform.

## Proof

Let $T = \left({S, \tau}\right)$ be totally disconnected.

Then by definition its components are singletons.

Thus by definition each of its connected sets are degenerate.

$\blacksquare$