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 $x$.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Paracompactness