Components are Open iff Union of Open Connected Sets

Theorem
Let $T = \struct{S, \tau}$ be a topological space.


 * (1) $\quad$ The components of $T$ are open.


 * (2) $\quad S$ is a union of open connected sets of $T$.

Also see

 * Path Components are Open iff Union of Open Path-Connected Sets, an analogous result for path components