Category:Union of Connected Sets with Non-Empty Intersections is Connected

This category contains pages concerning Union of Connected Sets with Non-Empty Intersections is Connected:

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

Let $I$ be an indexing set.

Let $\AA = \family {A_\alpha}_{\alpha \mathop \in I}$ be an indexed family of subsets of $S$, all connected in $T$.

Let $\AA$ be such that no two of its elements are disjoint:

$\forall B, C \in \AA: B \cap C \ne \O$

Then $\ds \bigcup \AA$ is itself connected.