Limit 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 adding its limit points.

Read more about Limit Point:  Definition, Types of Limit Points, Some Facts

Famous quotes containing the words limit and/or point:

    There is no limit to what a man can do so long as he does not care a straw who gets the credit for it.
    —C.E. (Charles Edward)

    How oft when men are at the point of death
    Have they been merry! which their keepers call
    A lightning before death: O, how may I
    Call this a lightning? O my love! my wife!
    Death, that hath sucked the honey of thy breath,
    Hath had no power yet upon thy beauty:
    Thou art not conquered; beauty’s ensign yet
    Is crimson in thy lips and in thy cheeks,
    And death’s pale flag is not advanced there.
    William Shakespeare (1564–1616)