Sentence examples for be a partial ordering from inspiring English sources

Let ((X,d)) be a partial ordering cone metric space over the Banach algebra (mathcal{A}).

Let X be a nonempty set, and ⪯ be a partial ordering on X.

Throughout, we will suppose that is strongly minihedral cone in with nonempty interior and be a partial ordering with respect to.

Let E be a locally convex Hausdorff tvs with its zero vector θ, P a proper, closed and convex pointed cone in E with intP ≠ ∅ and ≼ be a partial ordering with respect to P. Let (X, d) be a tvs-cone metric space with a solid cone P and let be a collection of nonempty subsets of X.

(X) is the (sin (1/x))-curve, defined to be the union (Acup Ssubseteq mathbb{R }^2,) where (A={0}times [-1,1]) and (S={langle x,sin (1/x)rangle : 0be a partial ordering.

Let (preceq) be a partial ordering on A. Let (F Atimes Arightarrow A) be a function for which F has mixed mixed monotone property and satisfies the following condition: G(F x,y), F x,y), F u,v),ks) * G(F y,x), F y,x), F v,u),ks) ge G x, x, u,s)*G y, y, v,s),for all (x,y,u,vin A,, s > 0) such that (xpreceq u) and (y succeq v), and (0< k <1) and (F(Atimes A subseteq A).

Let ⪰ be a partial order on B satisfying that ( B, ⪰ ) is a partially ordered vector space.

Let be a partial order relation on.

Let ( X, ⪯ ) be a partial ordered set.

Let ⪯ be a partial order on X.

Let (ll ) be a partial order relation on (mathbb R ).