Definition:Star (Topology)

Definition
Let $S$ be a set.

Let $\mathcal C$ be a cover for $S$.

Let $x \in S$.

The star of $x$ (with respect to $\mathcal C \ $) is defined as:
 * $\displaystyle x^* := \bigcup \left\{{U \in \mathcal C: x \in U}\right\}$

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