Definition:Star Shaped Set

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Let $V$ be a vector space over a field $K$.

Let $W \subseteq V$ be a subset of $V$.

Then $W$ is called a star shaped set if and only if:

$\forall x \in W: -x \in W$

where $-x$ is the negative of $x$.

Also known as

Sometimes one occurs the hyphenated form, i.e. star-shaped set.

A star shaped set is also known as a balanced set.