Definition:Star (Topology)

Definition
Let $S$ be a set.

Let $\CC$ be a cover for $S$.

Let $x \in S$.

The star of $x$ (with respect to $\CC$) is defined as:
 * $\ds x^* := \bigcup \set {U \in \CC: x \in U}$

That is, the union of all sets in $\CC$ which contain $x$.