Sentence examples for be any compact set from inspiring English sources

Let (S_{f}^{prime}) be any compact set contained in (S_{f}^{0}).

Let (Ksubset mathbb{R }^{d}, dge 2,) be any compact set and (Vert pVert _K:=sup _{mathbf{x}in K}|p(mathbf{x})|) the usual supremum norm on (K).

for some sequence, where is any compact set in.

Then, there exists a sequence, as such that uniformly on as, where is any compact set in.

Then, for any sequence, there exist a subsequence of and a function continuous in such that uniformly on as, where is any compact set in.

This Julia set is the attractor of the IFS J λ = { Q ⊂ C : f 1 ( z ) = z − λ, f 2 ( z ) = − z − λ } where Q is any compact set such that f i ( Q ) ⊂ Q for i = 1, 2, and the two branches ± z − λ of the inverse of z ↦ z 2 + λ are continuous on Q.

(a) Let (f(t)in C R,R^{n})), (f(t)) is almost periodic if only if (x t)) is bounded and uniformly continuous on R.   (b) Let (f:Rtimes Srightarrow R^{n}) be almost periodic in t uniformly with respect to (xin Ssubset R^{n}), where S is any compact set of (R^{n}).

Let (f(t)in C R,R^{n})), (f(t)) is almost periodic if only if (x t)) is bounded and uniformly continuous on R. Let (f:Rtimes Srightarrow R^{n}) be almost periodic in t uniformly with respect to (xin Ssubset R^{n}), where S is any compact set of (R^{n}).

The hull of f, denoted by (H f)), is defined by H f)= Bigl{ g(n,x):lim_{krightarrowinfty}f(n+tau_{k},x =g(n,x) text{ uniformly on } Ztimes S Bigr}, for some sequence ({tau_{k}}), where S is any compact set in D.

In reference to the function f ∈ L loc 1 ( R, E ) Open image in new window, where E is any compact set of R Open image in new window, we associate the translation f h ∈ L loc 1 ( R, E ) Open image in new window such that f h (t) = f(t + h), for each t ∈ R Open image in new window.

Let K ⊂ Q T be an any compact set.