Sentence examples for be a nonempty unbounded from inspiring English sources

Let be a nonempty unbounded closed convex set.

Let be a real reflexive Banach space with dual space, and let be a nonempty unbounded closed convex subset with.

Corollary 3.5 Let E be a real Banach space and C be a nonempty weak* closed convex unbounded subset of E ∗ ∗.

In this paper, the time scale considered is unbounded above, and for each interval of, we denote I T = I ∩ T. Let be a nonempty closed subset (time scale) of ℝ.

The only substantive requirement introduced by (5) is that there be a nonempty positive analogy.

Let X be a nonempty finite subset of the sphere of dimension n−1, where n⩾3.

Let be a nonempty poset.

Throughout this paper, G denotes an unbounded set of R + : = [ 0, ∞ ) such that s + t ∈ G for all s, t ∈ G and s − t ∈ G for all s, t ∈ G with s ≥ t (often G = N 0 or R + ). Let C be a nonempty subset of a Banach space X and T : C → C a mapping.

For each index τ ∈ I (T ), let T ⊆ T be a nonempty subset of associated elements.

Scott proved that if A is a nonempty proper subset of λ-terms that is closed under equality then A is not recursive.

A finite set of examples E, E = E + ∪ E − where E + is a nonempty set of positive examples, and E − is a set of negative examples.