在数学中，非正式的说在拓扑空间X中的一个集合S的极限点（limit point），就是可以被S中的点（不包含x本身）随意“逼近”的点。这个概念有益的推广了极限的概念，并且是诸如闭集和拓扑闭包等概念的基础。实际上，一个集合是闭合的当且仅当他包含所有它的极限点，而拓扑闭包运算可以被认为是通过增加它的极限点来扩充一个集合。

一个有关的概念是串行的聚集点（cluster point）或会聚点（accumulation point）。

In mathematics, a limit point of a set S in a topological space X is a point x (which is in X, but not necessarily in S) 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 uniting it with its limit points.