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Star RefinementIn 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 of X, with index set I, the star of x with respect to the cover is the set of i in I such that - x is in Ui.
For each x we can take the union of the sets in its star, say Vx. The condition on an open cover - Wj
for j in J to be a star refinement of the Ui is then - each Wj is contained in some Ui (refinement condition), and
- each set taken Vx with respect to the Wj is contained in a Ui (star condition).
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