In mathematics, a nonempty subset of a group is said to be symmetric if it contains the inverses of all of its elements.

Definition

In set notation is called

is a subset of a vector space is said to be a if it is symmetric with respect to the additive group The

Sufficient conditions

Arbitrary unions and intersections of symmetric sets are symmetric.

Any vector subspace in a vector space is a symmetric set.

Examples

are symmetric sets.

Any balanced subset of a real or complex vector space is symmetric.

See also

References

• R. Cristescu, Topological vector spaces, Noordhoff International Publishing, 1977.