In mathematics, informally speaking, a limit point of a set S in a topological space X is a point x in X that can be "approximated" by points of S other than x as well as one pleases. 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.