Quasicomponent
= Quasicomponent
{title2=$Q_x=\bigcap\{U:x\in U,\ U\text{ clopen}\}$}
The quasicomponent of a point is the intersection of all its clopen neighborhoods. Every connected set containing the point lies in its quasicomponent, since a <clopen set> cannot split a connected set. In a compact Hausdorff space, quasicomponents equal <connected components> by the <Šura-Bura component lemma>.