Sentence examples for compact closure from inspiring English sources

Let M be a complete Riemannian manifold and D⊂M a smoothly bounded domain with compact closure.

A class of algebras is defined, with the property that every bounded set has compact closure, where the compatibility conditions are automatically satisfied.

Using different methods, we extend his result to preservation of entropy for αg when the subgroup of Aut(G) generated by the corresponding inner automorphism Adg has compact closure.

The proposed approach is essentially geometric and of independent interest, as it also addresses the abstract problem of characterizing the interior of a convex cone C which is the conical hull of a set continuously parametrized by a compact closure of an open set.

Then has compact closure in.

So, A d(G) has compact closure in GL ( g ) Open image in new window.

Then, for every (varepsilon in ;]0,1[,) all the components of the level sets ({zin { mathbb C}: |u z)|compact closures in ({mathbb D}) if and only if u is a Blaschke product and begin{aligned} limsup _{rrightarrow 1} |u(rxi )|=1, textit{ for } textit{ every }, xi in mathbb T. end{aligned}.

To rule out such examples Hawking and Ellis employ the requirement that a physically acceptable spacetime (M, gab) be locally inextendible, i.e., there is no open subset U ⊂ M with non-compact closure in M such that the sub-spacetime (U, g|U) affords an extension (U′, g′) in which the closure of the isometric image of U is compact.

A comparison of the new compact boundary closure with the original explicit boundary closure demonstrates the improved accuracy for the new compact boundary closure, while the behavior of the scheme across discontinuities appears unaffected.

If X is complete, then M is totally bounded if and only if M is relatively compact (its closure M̄ is a compact set).

The linear stability analysis results indicate that a linearly stable compact WENO boundary closure is achieved.