Sentence examples for a relatively dense set from inspiring English sources

For this, we recall the concept of a relatively dense set.

Since, for the above, there exists a relatively dense set such that (2.4).

In Definition 3.1, we require (E{varepsilon,f,S}) to be a relatively dense set.

Thus, for all, there exists a relatively dense set such that (2.11).

A continuous function is called almost periodic if for each there exists a relatively dense set such that (1.2).

A continuous function is called almost periodic in uniformly for if, for each and each compact subset, there exists a relatively dense set (1.3).

If (f,gin C mathbb{T}times D,mathbb{E}^{n})) are two synchronously local-almost periodic functions, then, for any (varepsilon>0), the intersection of ε-local translation numbers sets of f and g is a nonempty relatively dense set, i.e., (E{varepsilon,f,S}cap E{varepsilon,g,S}) is a nonempty relatively dense set.

Note that from Definition 2.1, one can derive some classical concepts of relatively dense set.

Through our investigations, we find that the relatively dense set should not be for (mathbb{T}) rather it should be for the set Π defined in Definition 1.1.

Hence, it is obvious that Definition 2.1 is so general that it can unify the concepts of relatively dense sets for many irregular time scales, it will be a useful tool to describe the almost periodicity of functions on a more comprehensive scope of time scales.

From Definitions 2.2-2.5 2.2-2.5ll see that by emploneng Definition 2.1, some newillnceptseef relathatly dense sets for various types of time scales can by demploying