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