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:
“The only limit to our realization of tomorrow will be our doubts of today. Let us move forward with strong and active faith.”
—Franklin D. Roosevelt (1882–1945)
“But you must pay for conformity. All goes well as long as you run with conformists. But you, who are honest men in other particulars, know, that there is alive somewhere a man whose honesty reaches to this point also, that he shall not kneel to false gods, and, on the day when you meet him, you sink into the class of counterfeits.”
—Ralph Waldo Emerson (1803–1882)