Star refinement

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In mathematics, in the study in topology of open covers of a topological space X, a star refinement is a particular kind of refinement of an open cover of X. Given x in X and an open cover {W_j} of X, with index set J consider then the union W^*(x) (called the star of x) of these of the sets W_j for which x is in W_j. An open cover {W_j} is a star refinement of the {U_i} if for each x in X the set W^*(x) is contained in a U_i, for some i (star condition).