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:
“Washington has seldom seen so numerous, so industrious or so insidious a lobby. There is every evidence that money without limit is being spent to sustain this lobby.... I know that in this I am speaking for the members of the two houses, who would rejoice as much as I would to be released from this unbearable situation.”
—Woodrow Wilson (1856–1924)
“For pain is perhaps but a violent pleasure? Who could determine the point where pleasure becomes pain, where pain is still a pleasure? Is not the utmost brightness of the ideal world soothing to us, while the lightest shadows of the physical world annoy?”
—Honoré De Balzac (1799–1850)