# Definition:Star (Topology)

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## 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 $x$.