Sentence examples for collection of closed from inspiring English sources

We investigate when the Ruelle operator corresponding to such a filter is a pure isometry, and then use that characterization to study the problem of when a collection of closed subspaces, which satisfies all the conditions of a GMRA except the trivial intersection condition, must in fact have a trivial intersection.

Actually, they proved this result for alternating projections between any finite collection of closed convex sets.

The union of a countable collection of closed complete pluripolar sets in (mathbb {P}^n) is a convergence set in (mathbb {P}^n).

The union of a countable collection of closed complete pluripolar sets in (mathbb {C}^n) is an affine convergence set in (mathbb {C}^n).

Thus, ({x^{uparrow}cap f bigvee_{X}S): xin S }) is a collection of closed subsets of (f bigvee_{X}S)).

The collection of closed subsets of Δ and the collection of open subsets of X (which are exactly the ranges of the mappings F and S) are complete lattices, closed under intersection and union respectively, and are mapped isomorphically onto one another by S and F. (See the supplement on ordering relations for further details).

Employing the various methods and techniques used in the vast literature on the subject of the closed-form evaluations series associated with the zeta functions, Srivastava and Choi (see [[20], Chapter 3], [[21], Chapter 3], and see also the related references therein) presented a rather extensive collection of closed-form sums of series involving the zeta functions.

We show that geometric duality theory is not restricted to real pre-ordered Banach spaces, as is done classically, but can be extended to real Banach spaces endowed with arbitrary collections of closed cones.

Mrs. Kaufman told a story about one of her first experiences, when the collection of the closed Perelman Toy Museum in Philadelphia was being sold.

For each x∈ΦB, let πB x) be the collection of all closed primary ideals contained in the maximal ideal M x)="x−1 0).

Let C ( E ) be a collection of all closed subsets of E. Definition 1.3 For two subsets X, Y of E, we write.