Star domain

In geometry, a set

in the Euclidean space

is called a star domain (or star-convex set, star-shaped set[1] or radially convex set) if there exists an

the line segment from

lies in

This definition is immediately generalizable to any real, or complex, vector space.

Intuitively, if one thinks of

as a region surrounded by a wall,

is a star domain if one can find a vantage point

from which any point

A similar, but distinct, concept is that of a radial set.

Given two points

in a vector space

(such as Euclidean space

), the convex hull of

is called the closed interval with endpoints

{\displaystyle \left[x,y\right]~:=~\left\{tx+(1-t)y:0\leq t\leq 1\right\}~=~x+(y-x)[0,1],}

A subset

of a vector space

the closed interval

is star shaped and is called a star domain if there exists some point

A set that is star-shaped at the origin is sometimes called a star set.

[2] Such sets are closely related to Minkowski functionals.