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; beautys ensign yet
Is crimson in thy lips and in thy cheeks,
And deaths pale flag is not advanced there.”
—William Shakespeare (15641616)