Star region

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star-shaped set with the center of its interior (green) is a star region

In mathematics , a star-shaped set is understood to be a subset of the , to which there is a point (a star center or a star center ) from which all points of the set are "visible", that is, every straight connection from to any one Point is completely in .

If a star-shaped set is also open , one speaks of a star region .

Formal definition

A set is called a star , if there is one , so that the route for all

is a subset of .

Remarks

  • Every non-empty convex set is star-shaped.
  • The set of possible star centers is also called the center of the set. One can show that it is always convex. A set coincides with its center if and only if it is convex.
  • Star-shaped sets are contractable . It follows:
  • Star-shaped sets are simply connected , i.e. especially path-connected .
  • A star region is an area .

See also

literature

Web links