# bounded set

(redirected from Bounded subset)

## bounded set

[¦bau̇n·dəd ′set]
(mathematics)
A collection of numbers whose absolute values are all smaller than some constant.
A set of points, the distance between any two of which is smaller than some constant.
References in periodicals archive ?
epsilon]](w)y)(t) : y [member of] D(w)} is the image of a bounded subset of E, then [Z.
This is a closed and bounded subset of the space of d x (d + 1) matrices, hence it is compact with respect to the standard topology.
Let A be an open bounded subset of [OMEGA] such that K [subset] A: we recall that [W.
Liu) Let X be a Banach space, and let K be a nonempty closed convex and bounded subset of X.
n]) is called a Mackey-Cauchy sequence in A if there exist a balanced and bounded subset B of A and for every [epsilon] > 0 a number [n.
p] is a uniformly bounded subset of the Banach Space.
Schaefer ) Let (B, | x |) be a normed linear space, H a continuous mapping of B into B which is compact on each bounded subset of B.
Utility correspondences used by Subiza (1994) in representation of acyclic preferences have the characteristic that each alternative is associated with an upper bounded subset of real numbers.
m](PP))} + b(P) with b bounded on any bounded subset of U([K.
If there exists a constant k [greater than or equal to] 0 such that [alpha](A(S)) [less than or equal to] k[alpha](S), for every countably bounded subset S [subset] D, then A is called a countably k-set contraction operator.
We will say that U satisfies the Darbo condition (with a constant k [greater than or equal to] 0) if for any bounded subset we have [chi](U(X)) [less than or equal to] k[chi](X).

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