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Title of Journal: Acta Math Hung

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Abbravation: Acta Mathematica Hungarica

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Springer Netherlands

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Weightable quasi-uniformities

Authors: Hans-Peter A. Künzi, Salvador Romaguera,

Publish Date: 2012/04/03
Volume: 136, Issue:1-2, Pages: 107-128
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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.



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