Star refinement

Star refinement

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"} iffor each "x" in "X" the set "W"*("x") is contained in a "U""i", for some "i" ("star condition").


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