Totally Disconnected Space is Punctiform

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

Then $T$ is punctiform.

Proof
Let $T = \left({X, \vartheta}\right)$ be totally disconnected.

Then by definition its components are singletons.

Thus by definition each of its connected subsets are degenerate.