Sentence examples for notion of completeness from inspiring English sources

"New York refuses a single logic, and it declines any notion of completeness," he concludes.

Model theory involves a notion of completeness and incompleteness that differs from axiomatizability.

First, what notion of completeness is being invoked here?

To this end, we introduce an appropriate notion of completeness and order-continuity.

In the literature, the notion of completeness for quasimetric spaces can be varied; see e.g. [5, 10, 11].

It is evident that in Theorem 2.2, the notion of completeness of the metric space ( X, d ) can be replaced by the notion of f-orbitally completeness.

Recently, Alam et al. [10] adopted the notions of completeness and continuity with respect to order-theoretic metrical structure, which run as follows.

It is well known (see, for instance, [3, 4]) that there exist many different notions of completeness for T0 qpm spaces.

Note also that a sequence in a qpm space is -convergent (resp., -convergent) to if and only if (resp.,. It is well known (see, for instance, [26, 27]) that there exists many different notions of completeness for quasimetric spaces.

(Note that our notion of (sequential) completeness of ((X,d)) coincides with the usual notion of right K- sequential) completeness of ((X,d^{-1})).) A quasi-metric space ((X,d)) is Smyth complete provided that every left K- sequentialin ((X,d)) is completenessof (tau_{d^{s}}) (compare Definition 8 in [4], [5], p.454, etc).

Cone metric spaces were introduced by Huang and Zhang in [1], where they investigated the convergence in cone metric spaces, introduced the notion of their completeness, and proved some fixed point theorems for contractive mappings on these spaces.