bilateralset

Bilateralset is a term that has appeared in multiple disciplines without a single, widely accepted definition. It combines bilateral, meaning two-sided or reciprocally related, with set, indicating a collection or family of items. In the absence of a standard definition, the meaning of bilateralset is best determined from context.

In mathematics and geometry, some authors use bilateralset to denote a subset that is invariant under a specified bilateral symmetry—such as reflection across a line or inversion about a point. In this usage, a bilateralset is a collection S in a space X for which applying the symmetry operation maps S onto itself. This gives S a two-sided or mirror-symmetric character.

In information science or graph theory, bilateralset may describe a collection of elements connected by bilateral (two-way) relations, or a relation that is symmetric, so that if a is related to b, then b is related to a. The term here is informal and often supplants more standard terms like symmetric set or bidirectional relation.

In biology or anatomy, the term can appear in descriptive passages to denote features that occur on both sides of a midline, i.e., bilateral features, though this is more usually described with the adjective bilateral rather than as a set.

Because bilateralset is not standardized, authors should define it explicitly when used. See also symmetry, bilateral, and set theory concepts of invariance and relation closure.