Star (topology)

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In the mathematical theory of the simplicial complexes , a star is a certain environment of a simplex.

Let be a simplicial complex and a set of simplices in .

The conclusion of is the smallest sub-simplicial complex of that contains. So it contains and all pages of simplizes in .

The (open) star of a simplex is the union of all simplices that contain as a side. The (open) star of is the union of the stars of all simplices from . A closed star is the closure of the star of .

The link from is the difference between the termination of the star of and the star of the termination of .

literature

Ralph Stöcker, Heiner Zieschang : Algebraic Topology. Teubner, Stuttgart 1988, ISBN 3-519-02226-5