Star domain

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In mathematics, a set S in the Euclidean space Rⁿ is called a star domain (or star-convex set) if there exists x₀ in S such that for all x in S the line segment from x₀ to x is in S. This definition is immediately generalizable to any real or complex vector space.

Contents 1 Properties 2 See also 3 References 4 External links

[edit] Properties

• Any convex set is a star domain.
• A cross-shaped figure is a star domain but is not convex.
• A plane is a star domain (being convex), but a plane without a point is not a star domain.
• The closure of a star domain is a star domain, but the interior of a star domain is not necessarily a star domain.
• Any star domain is a simply connected set.

[edit] See also

• Star polygon — an unrelated term

[edit] References

• Ian Stewart, David Tall, Complex Analysis. Cambridge University Press, 1983. ISBN 0-521-28763-4.

[edit] External links

Weisstein, Eric W., Star convex at MathWorld.