limit point

[Marquetta]

the mathematical value toward which a function goes as the independent variable approaches infinity

[MonicaLes]

A limit point (or accumulation point) is a point that is associated with a set in a topological space, such that every open set containing that point also contains an infinite number of distinct points from the set. In other words, regardless of how small the open interval around the limit point is, there are always other points from the set within this interval.

[VikaRip]

In mathematics, a limit point of a set S in a topological space X is a point x that can be approximated by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself. Note that x does not have to be an element of S. This concept profitably generalizes the notion of a limit and is the underpinning of concepts such as closed set and topological closure. Indeed, a set is closed if and only if it contains all of its limit points, and the topological closure operation can be thought of as an operation that enriches a set by adding its limit points.

[Gregory]

a point which lies in the closure of A{x} of a set A.