Sentence examples for local completeness from inspiring English sources

Assuming that is a locally complete locally convex space, the condition on local completeness of some related subsets is automatically satisfied.

However, we give the following examples of spaces which are not locally complete but the condition on local completeness of some related subsets is satisfied.

Recently, Qiu [18] obtained some versions of Ekeland's variational principle in locally convex spaces, which only need to assume local completeness of some related sets.

Local completeness is a very weak completeness property.

Therefore, by Ascoli's theorem and taking into account the local completeness of M ˆ, we get that P maps W into a compact subset of M ˆ.

The notion of local completeness has become important in all sorts of applications, for instance, in nonlinear distribution theory (see [1, 20] and the references therein), or as a context where existence and uniqueness for nonlinear integro-differential equations can be shown (see [21]).

However, as these individual characteristics are crucial for further investigations of local differences, completeness is important here.

Because the accuracy requirements for different scientific applications vary (11), CAMEO offers a variety of scores assessing different aspects of a prediction (coverage, local accuracy, completeness, responsiveness, etc).

For a Boolean local topos, ω-completeness will also ensure that all numerals are standard, so that numerals mean exactly what they are intended to mean.

As an application to the scattering problems, the decay of local energy and the completeness of wave operators are obtained.

EPR use this case to argue that one cannot maintain both an intuitive condition of local action and the completeness of the quantum description by means of the wave function.