Sentence examples for a directed subset from inspiring English sources

We then have a directed subset E ′ of F ( h ).

Under cases (i.b) and (ii), we can construct a directed subset of F ( h ), denoted by E ″, in such a way that for every x i ∈ E, there exists b i ∈ E ″ such that b i ≥ x i.f Since F ( h ) is a CPO, the supremum ⋁ E ″ is included in F ( h ).

U x is the union of all directed subsets of X including x as a bottom element.

( X, ≤ ) turns out to be a complete partially ordered set (CPO) if (i) X has a bottom element, ⊥; and (ii) for each directed subset D of X, the supremum exists.

Proof of Theorem 3 Here, we construct the directed subset E ″ ⊂ F ( h ) in such a way that for every x i ∈ E, there exists b i ∈ E ″ such that b i ≥ x i.

The basic definitions about coincidence points, g-orbital completeness of metric binary spaces, g-comparative mappings, directed subsets and regular spaces endowed with relations, were stated in the previous section.

Let (rhoinRe) (the class of all nonzero regular function modulars defined on a nonempty set Ω) and G be a directed graph defined on a subset C of (L_{rho}).

A function f from (D, ≤) into a complete lattice (E, ≤) is said to be continuous when it preserves the supremum of each ideal on D, where an ideal is an upward directed downward closed subset.

Then we need to show that each directed nonempty subset E of ε ( f ) has a supremum; i.e., ⋁ ε ( f ) E exists.

Now, take any directed nonempty subset E of ε ( F ).

More generally selective control is a computational challenge in a broad range of systems biology problems where intervention needs to be directed at subsets of a diverse population.