endset

Endset is a term encountered in several areas of mathematics and computer science, but it does not have a single universal definition. In practice, endset is used to denote a collection of endpoint-like elements associated with a given set, relation, or data structure. Because different authors and fields define it differently, the precise meaning of endset is context dependent and should be described alongside the surrounding concepts.

In order theory, endset of a subset A within a partially ordered set P is sometimes taken to mean the set of maximal elements of A; that is, elements a in A for which there is no element a′ in A with a < a′. This usage highlights the role of endset as signaling the “top” or terminal elements relative to the chosen order, and it can help characterize the boundary of A within P.

In topology and geometry, endset is occasionally used to refer to boundary or end points associated with a subset, such as points that lie on the edge of the closure or along a limiting process. Because there is no universally accepted standard, different texts may treat endset as equivalent to a boundary, the set of accumulation points, or a related notion of endpoints.

An example in a simple poset: if P is the natural numbers with the usual order and A = {1, 2, 3}, the endset in the maximal-elements sense would be {3}. In a topological setting, a subset like (0, 1) might be discussed in terms of its boundary points {0, 1} when endset is used informally.

Endset thus serves as a flexible, context-driven concept whose exact definition should be clarified in each use.