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:
“Can you find out the deep things of God? Can you find out the limit of the Almighty?”
—Bible: Hebrew, Job 11:7.
“The whole point of Camp is to dethrone the serious. Camp is playful, anti-serious. More precisely, Camp involves a new, more complex relation to the serious. One can be serious about the frivolous, frivolous about the serious.”
—Susan Sontag (b. 1933)