Sentence examples for be any compact subset from inspiring English sources

Let be any compact subset of such that for all and for all.

Let (mathcal{D}) be any compact subset of the real two-dimensional space.

Suppose that (Omega subset mathbb{R}) and K is any compact subset of Ω.

Let be a positive integer sequence such that,, and uniformly on as, where is any compact subset in and.

If K is any compact subset in U, then there is an (N_K>0) so large that, if (N ge N_K), then K is contained in (S_N).

A function is called (Bohr) almost periodic in uniformly in where is any compact subset if for each there exists such that every interval of length contains a number with the property that (2.3).

Since X can be seen as a retract of an open set in a normed space (namely, the space of bounded continuous real functions on X), one concludes that if K is any compact subset of X, then there exists a compact ANR C such that (Ksubset Csubset X).

A function (fin C mathbb{R}times Y,X)) is called (Bohr) almost periodic in (tinmathbb{R}) uniformly in (yin K) where (Ksubset Y) is any compact subset if for each (epsilon>0) there exists (l=l epsilon)>0) such that every interval of length l contains a number τ with the property that biglVert f(t+tau,y -f t,y)bigrVert+tau,y -f tuad (tinmathbb{R},y bigrVert

Definition 2.3. is the set of the Borel measurable functions which are bounded on any compact subset of.

The following inequality sup z ∈ K | F ( z ) | ≤ C ( K ) ∥ F ∥ L p ( D, dV ) which is valid for any compact subset K ⊂ D and for any holomorphic function F ∈ ϑ ( D ), shows that the Bergman space is a closed subspace of L q ( D, dV ).

It is easy to see that is a subset of We say that is a universal kernel if for any compact subset is dense in (see [13, Page 2652]).