Given a

bounded subset B C R and a configuration X [member of] Conf (R), let [#.

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 [5]) 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).