Sentence examples for be continuous and let from inspiring English sources

Example 3.3 Let g : R → R be continuous, and let f ( n, t ) = g ( t ).

Let (u:Xtimes Ylongrightarrowmathbb{R}) be continuous, and let (S: Xrightrightarrows Y) be continuous and nonempty compact-valued.

Let the functions ({p}:Irightarrow ( {0,infty } ) ) and (varphi Irightarrow J ) be continuous, and let the function (phi :Jrightarrowmathbb{R} ) be differentiable.

Let the function ({p}:Irightarrow ( {0,infty } ) ) be continuous, and let the functions (varphi Irightarrow J ) and (phi :Jrightarrowmathbb{R} ) be differentiable and twice differentiable, respectively.

Let N be a closed ball in AB, let (P: N rightarrow N) be continuous, and let PN be locally equicontinuous.

Let be a self-map on such that is continuous, and let be any self-map on that commutes with.

Assume that R and T are continuous and let the pairs (f,T) and (g,R) are compatible.

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.

observe that is continuous, and letting in (2.7), we have (2.8).

Taking into account (2.13) and (2.15) and the fact that is continuous and letting in (2.16), we get (2.17).

Let be continuous and convex, and let be convex of order such that for.