Sentence examples for be any closed subset from inspiring English sources

Let (Asubset X) be any closed subset.

For (jin J), (phi _{j} colon X rightarrow [0, infty )) will be the function defined by (phi _{j}(x) = phi _{1j}(x) + phi _{2j}(x)). Let (Asubset X) be any closed subset, and suppose that (phi _{1j}) and (phi _{2j}) are (rho _{j} -lsc.

We also construct some examples of extremizing sequences that prove that the limit spectrum can be essentially any closed subset of R+ that contains the spectrum of the limit sphere.

On the other hand, let be any closed bounded balanced subset of.

if the set ({xin X: varPsi (x cap Bneq varnothing}) is closed for any closed subset B in X. Definitions 1-8 have been introduced in [2, 3, 7] and are frequently used in the subsequent part of the article.

In addition, Let Q be any given closed subset of (mathbb{R}^{n}_ setminus {boldsymbol{0}}) and define gamma =inf_{boldsymbol{x}in Q} Vert boldsymbol{x} Vert _{infty }^{ overline{boldsymbol{upsilon }}}, which is used to design the switching signals in the following.

Let be a closed subset of,, and.

Let be a closed subset of with.

Let (mathcal{S}) be a closed subset of (mathbb{R}^{3}).

Let be a closed subset of a Banach space.

Let X be a closed subset of a Banach space.