Quasi-Metrizability of Bornological Biuniverses in ZF

A. Piękosz; E. Wajch

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arXiv · 1408.4823

Quasi-Metrizability of Bornological Biuniverses in ZF

A. Piękosz·E. Wajch

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Abstract

Hu's metrization theorem for bornological universes is shown to hold in ZF and it is adapted to a quasi-metrization theorem for bornologies in bitopological spaces. The problem of uniform quasi-metrization of quasi-metric bornological universes is investigated. Several consequences for natural bornologies in generalized topological spaces in the sense of Delfs and Knebusch are deduced. Some statements concerning (uniform)-(quasi)-metrization of bornologies are shown to be relatively independent of ZF.

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BibTeX RIS

A. Piękosz, E. Wajch. 2014-08-20. Quasi-Metrizability of Bornological Biuniverses in ZF. https://arxiv.org/abs/1408.4823

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