Sentence examples for for every closed from inspiring English sources

For every closed subspace A of an L-ts (X,τ), dimA ≤ dimX.

if ({x in X : F x cap Cneemptyset}) is closed for every closed set (Csubset Y).

Observe that Condition (iii) in the previous theorem is satisfied if (x mapsto H t,s,x)) is upper semi-continuous (i.e. ({x in E : H t,x capap B neemptyset}) is closed for every closed (Bsubset E)) a.e.

if, for every open (Usubset Y), the set (varphi^{-1}(U)) is open in X or equivalently if, for every closed (Usubset Y), the set (varphi_^{-1}(U)) is closed in X.

if, for every closed (Usubset Y), the set (varphi^{-1}(U)) is closed in X or equivalently if, for every open (Usubset Y), the set (varphi_^{-1}(U)) is open in X.

if, for every open (Usubset Y), the set (varphi^{-1}(U):={xin X;> varphi(x)subset U}) is open in X or equivalently if, for every closed (Usubset Y), the set (varphi^{-1}_(U):={xin X;> varphi(x cap Uneemptyset}) is closed in X.

For every meeting closed pursuant to paragraphs (1) through (10) of subsection (c), the General Counsel or chief legal officer of the agency shall publicly certify that, in his or her opinion, the meeting may be closed to the public and shall state each relevant exemptive provision.

But for every loophole closed in the wake of the nation's latest gun mayhem — from Columbine to the D.C. sniper, ad infinitum — others beg attention in the crazy quilt of state and federal regulations cynically manipulated by the gun lobby.

If is a metrically convex cone metric space, that is, if for each there is such that, we do not know whether (2.4) holds for every nonempty closed subset in (see [8]).

Borrowing an age-old tactic from Avon and Tupperware, Harris recruited a network of independent sales reps to sell PCs to their friends, relatives and co-workers, getting commissions of $150 or more for every deal closed.

A Banach space is said to have normal structure (NS) (resp., weak normal structure ( -NS)) if for every bounded closed (resp., weakly compact) convex subset of with there exists such that.