Sentence examples for be a qpm space from inspiring English sources

Let be a qpm space.

Indeed, it is obvious that if is a qpm space, then satisfies conditions (Q1) and (Q2), whereas Example  3.2 of [5] shows that there exists a qpm space such that does not satisfy condition (Q3), and hence it is not a Q-function on.

Let be a complete qpm space.

Let be a weighted qpm space.

(a) Let be a weightable qpm space with weighting function.

Let be a complete qpm space, q a Q-function on, and a multivalued map such that for each and, there is satisfying (3.3).

A qpm space is said to be complete if every Cauchy sequence is -convergent, where a sequence is called Cauchy if for each there exists such that whenever.

A qpm space is a pair such that is a set and is a qpm on.

Let q be a Q-function on a qpm space.

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.

A -function on a qpm space is a function satisfying the following conditions: (Q1), for all, (Q2) if, and is a sequence in that -converges to a point and satisfies, for all, then, (Q3) for each there exists such that and imply.