Sentence examples for be a semigroup with from inspiring English sources

Let be a semigroup with identity.

Let be a semigroup with identity and functions satisfying the inequality (2.19).

Let be a semigroup with identity and functions satisfying condition (1.4), that is, (2.20).

In this section, let be a semigroup with identity and a function with.

If (Pi^) is a semigroup with negative-direction (or positive-direction), then δ is a negative-direction shift operator (or a positive-direction shift operator).

Then a subspace of is left (resp., right) translation invariant if (resp., for all where and, A semitoplogical semigroup is a semigroup with Hausdorff topology such that for each the mappings and from into are continuous.

Let G be a semitopological semigroup, i.e., G is a semigroup with a Hausdorff topology such that for each t ∈ G, the mappings s ↦ s t and s ↦ t s from G to G are continuous.

Let S be a semitopological semigroup, i.e., S is a semigroup with a Hausdorff topology such that for each s ∈ S, the mappings s ↦ t s and s ↦ s t from S to S are continuous, and let B C ( S ) be the Banach space of all bounded continuous real-valued functions with supremum norm.

Let C be a nonempty bounded subset of a Banach space E. Let G be a semitopological semigroup, i.e., G is a semigroup with a Hausdorff topology such that for s ∈ G the mappings s ↦ s t and s ↦ t s from G to G are continuous.

Let ( S ; ⋄ ) and ( S ˜ ; ⋄ ) be a semigroup and a group with semigroup operation ⋄, respectively.

Lemma 3.1 Let ( X, d ) be a complete bounded metric space with uniform normal structure, and let ℑ = { F ( t ) : t ∈ G } be a semigroup on X × X × X with property.