Journal Title Title of Journal: Acta Math Hung Search In Journal Title: Abbravation: Acta Mathematica Hungarica Search In Journal Abbravation: Publisher Springer Netherlands Search In Publisher: DOI 10.1007/s12307-014-0164-4 Search In DOI: ISSN 1588-2632 Search In ISSN:
Search In Title Of Papers:

# Weightable quasi-uniformities

## Abstract

The authors study quasi-uniformities that are generated by a family of weightable quasi-pseudometrics. Each totally bounded quasi-uniformity is of this kind. In some sense, which is described in this article, a weightable quasi-uniformity is fairly symmetric, with the associated weights generating small symmetrizers.In the second part of the article we continue our investigations by generalizing a subclass of weightable quasi-uniformities to a more abstract level. We introduce the concept of a t-symmetrizable quasi-uniformity, that is, a quasi-uniformity $${\mathcal{U}}$$ possessing the property that there exists a totally bounded quasi-uniformity $${\mathcal{Z}}$$ such that $${\mathcal{U}}\vee {\mathcal{Z}}$$ is a uniformity. It turns out that t-symmetrizable quasi-uniformities are closely related to quasi-uniformities generated by weightable quasi-pseudometrics possessing bounded weight functions. We show that several results that were originally proved for weightable quasi-pseudometrics (with bounded weights) still hold in a such apparently broader context.

## References

.
Search In Abstract Of Papers:

##### Search Result:

Help video to use 'Paper Search Console'