Sentence examples for necessarily closed from inspiring English sources

The convex hull of a finite subset is not necessarily closed, and likewise the closed convex hull of A, denoted (overline{co}(A) ), is the intersection of all closed convex subsets containing A.

The evolution of language is necessarily closed off from us.

There were crops to be tended during the summer, so schools necessarily closed for three months.

Also today, the mayor signaled that he did not believe that the Conservative Party endorsement was necessarily closed to him, contending that if the party were to have a primary, he would win it.

Recall that Tx is not necessarily closed but it is bounded.

Assumption (A) holds for a wide class of (not necessarily closed) sets including these classical models.

And, Mr. Musto noted, the Chelsea was not necessarily closing.

Their responses Tuesday did not necessarily close the book on the anchoring issue.

Relations between the folkies and the Beats in New York were not necessarily close or even harmonious.

Yet for all the camaraderie, most residents add that they are not necessarily close friends.

The imprinting of the young bird on one object necessarily closes down the possibility of its imprinting on others, as these will always be relatively less familiar.