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 are two types of happiness and I have chosen that of the murderers. For I am happy. There was a time when I thought I had reached the limit of distress. Beyond that limit, there is a sterile and magnificent happiness.”
—Albert Camus (1913–1960)
“Where there is no style, there is in effect no point of view. There is, essentially, no anger, no conviction, no self. Style is opinion, hung washing, the calibre of a bullet, teething beads.... One’s style holds one, thankfully, at bay from the enemies of it but not from the stupid crucifixions by those who must willfully misunderstand it.”
—Alexander Theroux (b. 1940)