- Star domain
In
mathematics , a set in theEuclidean space R"n" is called a star domain (or star-convex set) if there exists in such that for all in theline segment from to is in This definition is immediately generalizable to any real or complexvector space .Intuitively, if one thinks of as of a region surrounded by a fence, is a star domain if one can find a vantage point in from which any point in is within line-of-sight.
Examples
* Any line or plane in R"n" is a star domain.
* A line or a plane without a point is not a star domain.
* If "A" is a set in R"n", the set :: : obtained by connecting any point in "A" to the origin is a star domain.Properties
* Any
non-empty convex set is a star domain. A set is convex if and only if it is a star domain in respect to any point in that set.
* Across -shaped figure is a star domain but is not convex.
* 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 contractible set, via a straight-linehomotopy . In particular, any star domain is asimply connected set .
* The union and intersection of two star domains is not necessarily a star domain.ee also
*
Art gallery problem
*Star polygon — an unrelated term
*Star-shaped polygon References
* Ian Stewart, David Tall, "Complex Analysis". Cambridge University Press, 1983. ISBN 0-521-28763-4.
* C.R. Smith, "A characterization of Star-shaped sets",
American Mathematical Monthly , Vol. 75, No. 4 (April 1968). pp. 386.External links
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