Star refinement

In mathematics, specifically in the study of topology and open covers of a topological space X, a star refinement is a particular kind of refinement of an open cover of X.

The general definition makes sense for arbitrary coverings and does not require a topology. Let $X$ be a set and let $\mathcal U=(U_i)_{i\in I}$ be a covering of $X$ , i.e., $X=\bigcup_{i\in I}U_i$ . Given a subset $S$ of $X$ then the star of $S$ with respect to $\mathcal U$ is the union of all the sets $U_i$ that intersect $S$ , i.e.:

单词	Star refinement
释义	Star refinement 英语百科 Star refinement In mathematics, specifically in the study of topology and open covers of a topological space X, a star refinement is a particular kind of refinement of an open cover of X. The general definition makes sense for arbitrary coverings and does not require a topology. Let $X$ be a set and let $\mathcal U=(U_i)_{i\in I}$ be a covering of $X$ , i.e., $X=\bigcup_{i\in I}U_i$ . Given a subset $S$ of $X$ then the star of $S$ with respect to $\mathcal U$ is the union of all the sets $U_i$ that intersect $S$ , i.e.:
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