**Authors: **HansPeter A Künzi Salvador Romaguera

**Publish Date**: 2012/04/03

**Volume:** 136, **Issue:** 1-2, **Pages:** 107-128

## Abstract

The authors study quasiuniformities that are generated by a family of weightable quasipseudometrics Each totally bounded quasiuniformity is of this kind In some sense which is described in this article a weightable quasiuniformity is fairly symmetric with the associated weights generating small symmetrizersIn the second part of the article we continue our investigations by generalizing a subclass of weightable quasiuniformities to a more abstract level We introduce the concept of a tsymmetrizable quasiuniformity that is a quasiuniformity mathcalU possessing the property that there exists a totally bounded quasiuniformity mathcalZ such that mathcalUvee mathcalZ is a uniformity It turns out that tsymmetrizable quasiuniformities are closely related to quasiuniformities generated by weightable quasipseudometrics possessing bounded weight functions We show that several results that were originally proved for weightable quasipseudometrics with bounded weights still hold in a such apparently broader context

**Keywords:**