Limit Point

Also found in: Dictionary, Thesaurus, Wikipedia.

limit point

[′lim·ət ‚pȯint]

Limit Point


(or accumulation point). A limit point of a set A in a metric space is a point ξ in a space such that arbitrarily close to ξ there are points in A distinct from ξ. In other words, ξ is a limit point if any neighborhood of ξ contains an infinite number of points in A. A characteristic property of ξ is the existence of at least one sequence of distinct points of A that converges to ξ.

A limit point of a set does not have to belong to the set. Thus, every point on the real axis is a limit point for the set of rational points, because for every number—rational or irrational—we can find a sequence of distinct rational numbers that converges to it. Not every infinite set has a limit point; the set of integers, for example, lacks such a point. Every infinite bounded set of a Euclidean space, however, has at least one limit point.


Aleksandrov, P. S. Vvedenie v obshchuiu teoriiu mnozhestv i funktsil Moscow-Leningrad, 1948.
References in periodicals archive ?
If the sets A and B have limit points in D, then the tuple [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is diskcyclic on H.
0]-axiom implies the equivalence of the concept of limit point of a set with that of vg-[T.
iii) a dense limit point, or shortly d-limit point, of A if it is a limit point of A [intersection] [T.
To compute the optimal limit points maximizing Equation [5], a generalization of the algorithm given previously is applied.
Then, the limit points of the zeros of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
Then [LAMBDA] has no limit points, and there exists an [epsilon] > 0 such that [absolute value of [y.
CO] ratio, the ignition temperature (temperature at which limit point observed), decreases.
Theorem 1 is equivalent to saying that any limit point of {N, (1)ln} belongs to the interval [1/4, 3/4].
You must learn to match your speed to the speed at which the limit point appears to move.
Additional Key Words and Phrases: Continuous spectrum, eigenfunction norm, eigenvalue, limit circle, limit point, oscillatory, singular endpoints, spectral density functions, Sturm-Liouville problems
In The Alchemist, conspiracies expand indefinitely, with no limit point beyond which strategies of play will cease their oscillation.
There is no first such number but 0 provides a limit point lying on the boundary of the closed interval [0, 1].