twoend

Twoend is an informal term used to describe a concept that appears in topology, geometric group theory, and computing when two extremities or endpoints are involved. In mathematical literature the standard spelling is two-ended (with a hyphen); twoend is occasionally seen in informal writing or as a project name.

In topology, ends of a space capture different ways to go to infinity. A space has two ends if, after removing any compact subset, the remainder breaks into exactly two unbounded connected components. The real line is the simplest example, having two ends. Other spaces may have one end (for instance, the plane) or infinitely many ends (such as certain infinite trees). The notion helps describe the large-scale structure of spaces and figures prominently in ideas like the Freudenthal compactification.

In geometric group theory, the concept translates to the ends of a finitely generated group, defined via its Cayley graph. The number of ends of a group is 0, 1, 2, or infinite. Groups with more than one end admit particular decompositions, reflecting a link between end behavior and algebraic structure. This connection provides tools for understanding how groups split and expand at infinity.

In computing and networking, two-ended or double-ended configurations refer to systems or channels with two endpoints, such as communication links or data structures that allow operations at both ends. The exact meaning depends on context, and the term two-ended is less common than more specific terms like deque (double-ended queue) in programming.

See also: ends (topology); ends of groups; double-ended queue.