Sentence examples for order dense from inspiring English sources

An ideal F ˜ in F is said to be order dense in F if, for every 0 ≤ x ∈ F, there exists an upwards directed system ( x τ ) ⊂ F ˜ such that 0 ≤ x τ ↑ x, and is said to be super order dense if this condition holds for increasing sequences.

Moreover, L w 1 / p ( ν 1 ) has the Fatou property and L 1 / p ( ν 1 ) is order dense in L w 1 / p ( ν 1 ) (see the comments before Section 4 in [21]).

Theorem 1 Let p > 1 and let F be a p-convex Banach lattice with p-convexity constant equal to 1, having the Fatou property and such that its σ-order continuous part F a is an order dense subset.

Suppose that F a is order dense in F. Consider a closed subspace G such that F a ⊂ G ⊂ F. Then the following statements are equivalent for a Fatou operator T : G → E. (1) T | F a is p-concave.

Furthermore, a representation theorem for the class of σ-Fatou Banach lattices F with the σ-order continuous part as a super order dense ideal in F, using again vector measures on δ-rings, is established in [[13], Proposition 6.1].

In this case, every Banach lattice F with the Fatou property, and such that its σ-order continuous part is an order dense subset in F, can be represented as a space L w 1 for some vector measure ν defined on a δ-ring.

The morphology and microstructure of the hierarchical SnO2 architecture showed that flower-like hierarchical SnO2 architecture with six similar petals were organized by large scale uniformity and ordered dense nanorods arrays with a diameter of 10 15 nm and length of about 200 nm.

On the other hand, the overwhelmingly large number of cryptic (i.e. false positive) binding sites that occur throughout the eukaryotic genome tend to be masked and inaccessibly wrapped in nucleosome particles, which are themselves stacked into a higher-order, dense chromatin configuration.

You can choose a "compact" feed, a "cozy" feed or a "comfortable" feed, listed in order from dense to sparse.

Large-area, continuous, smooth, highly ordered, and dense nanowire and nanocable arrays can be seen in Figure 3a, c, respectively.

In ordered and dense environments like urban cities, sound seems to become even more diffuse and deeper-reaching.