Sentence examples for of every compact from inspiring English sources

If (Z) is locally compact and Hausdorff, this condition is equivalent to the requirement that the preimage of every compact subset of (Z) under (f) be compact in (Y) (see, e.g., [13], Chap. I, pp. 72, 75, 77]).

Proof Because F has a closed graph, the pre-image under F of every compact set is closed (see [38, Theorem 4] ).

Because F has a closed graph, the pre-image under F of every compact set is closed (see [38, Theorem 4]).

Applying again Dini's result we get the uniform convergence of ((h_{k})) on every compact subset of ((0,T]).

By fϵ lbv(I, X), we mean that f is a function of a real interval I to a Banach space X, with bounded variation on every compact subinterval of I; to such f, an X-valued measure df, called its differential measure, classically corresponds.

This formula holds locally uniformly, that is, on every compact subset of the complex plane.

This mentioned convergence is uniform on every compact subset of complex plane.

Considering Lemma 2.2, it follows that (lim_{nrightarrowinfty}mathcal{L}_{n}^{rho}(t^{i};x)=x^{i}), (i=0,1,2), uniformly on every compact subset of (R_{0}^).

A sequence { f n } n ∈ N ⊆ C ( X ) converges to g ∈ C ( X ) if and only if { f n } n ∈ N uniformly converges to g on every compact subset of X.

Let ( f n ) n ∈ N be a sequence in A log α with sup n ∈ N ∥ f n ∥ A log α ≤ M and f n → 0 uniformly on every compact subset of D as n → ∞.

A mapping g : I → E, − ∞ < min I < sup I ≤ ∞, is said to be locally integrable in HK, HL, Bochner or Riemann sense if g is HK, HL, Bochner or Riemann integrable on <span class="lh">every compact subinterval of I.