Weightable quasi-uniformities

作者：Kuenzi H P A; Romaguera S

来源：Acta Mathematica Hungarica, 2012, 136(1-2): 107-128.

DOI：10.1007/s10474-012-0213-8

• weightable quasi-pseudometric
• weightable quasi-uniformity
• t-symmetrizable quasi-uniformity
• Wijsman quasi-pseudometric
• totally bounded

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. %26lt;br%26gt;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 possessing the property that there exists a totally bounded quasi-uniformity such that 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.

• 出版日期2012-7