bounded

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bounded

(theory)
In domain theory, a subset S of a cpo X is bounded if there exists x in X such that for all s in S, s <= x. In other words, there is some element above all of S. If every bounded subset of X has a least upper bound then X is boundedly complete.

("<=" is written in LaTeX as \subseteq).
References in periodicals archive ?
The boundedness of G in Assumption 4.1 and the stability estimates in (6.2) and (6.3) allow us to control Ge and G[[partial derivative].sub.t]e.
It is noted the boundedness of [[alpha].sub.Ui], [[??].sub.Ui], [[alpha].sub.[psi]Ti], and [[??].sub.[psi]Ti] ensures the boundedness of [[alpha].sup.c.sub.Ui], [[??].sup.c.sub.Ui] [[??].sup.c.sub.Ui], and [[??].sup.c.sub.[psi]Ti] by Lemma 9.
Furthermore, because [[theta].sub.[sigma]] and [[eta].sub.[sigma]] are bounded, the boundedness of the estimated parameters [[??].sub.[sigma]](k) and [[??].sub.[sigma]](k) is guaranteed by [mathematical expression not reproducible].
So, V(t) is uniform ultimate boundedness. Combining (17) and (36), there is
Medina, "Existence and boundedness of solutions for nonlinear volterra difference equations in banach spaces," Abstract and Applied Analysis, vol.
In this paper, we consider some characterizations of boundedness in [N.sub.*](D) and [N.sup.p](D) (p > 1).
For [II.sub.1], [L.sup.2] boundedness of SL and the Holder inequality tell us
If we assume that [mathematical expression not reproducible] and 0 [less than or equal to] [[alpha].sub.p] [??] 1 then, defining the norms according to (2.5), the boundedness of both [mathematical expression not reproducible] and (div u, q) + (div v, q) is obvious.
Next, we prove the boundedness of solutions by considering the following function:
It follows from (41) and the boundedness of {([u.sub.n], [v.sub.n])} in [D.sub.K]([OMEGA]) that
Ljubisa D.R Koeinac shared his thoughts and research work with audience on 'Function Spaces and Boundedness Properties'.