Union of Connected Sets with Common Point is Connected/Proof 2

Theorem

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

Let $\family {B_\alpha}_{\alpha \mathop \in A}$ be a family of connected sets of $T$.

Let $\exists x \in \ds \bigcap \family {B_\alpha}_{\alpha \mathop \in A}$.

Then

$\ds \bigcup \family {B_\alpha}_{\alpha \mathop \in A}$ is a connected set of $T$.

Proof

Follows immediately from Union of Connected Sets with Non-Empty Intersections is Connected.

$\blacksquare$