Accumulation Point

A point x in a topological space is an accumulation (limit) point of a set S if every neighbourhood of x contains at least one point of S distinct from x itself; equivalently x belongs to the derived set S' of limit points.

A point such that every neighborhood of it contains at least one point of a given set distinct from the point itself (or infinitely many points, depending on convention); equivalently a point in the closure of the set minus any isolated occurrences.

A point such that every neighborhood contains infinitely many distinct points of a given set; equivalently a limit point of the set that is not isolated, often used to describe limiting behavior of sequences and subsets.