Geodesic
Quasi-Metrizability of Bornological Biuniverses in ZF
Journal of convex analysis, Tome 22 (2015) no. 4, pp. 1041-106
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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 and several relevant results independent of ZF are obtained. In particular, some theorems of Garrido and Meroño that contain necessary and sufficient conditions for a bornology in a metric space to be uniformly metrizable are generalized to quasi-metric bornological universes in ZF, while some other theorems of Garrido and Meroño are shown to fail in a model for ZF.
Classification : 54E55, 54A35, 54E35, 54E99
Mots-clés : Bornology, bitopological space, quasi-metric, ZF 
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     author = {A. Piekosz and E. Wajch},
     title = {Quasi-Metrizability of {Bornological} {Biuniverses} in {ZF}},
     journal = {Journal of convex analysis},
     pages = {1041--106},
     year = {2015},
     volume = {22},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a7/}
}
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A. Piekosz; E. Wajch. Quasi-Metrizability of Bornological Biuniverses in ZF. Journal of convex analysis, Tome 22 (2015) no. 4, pp. 1041-106. http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a7/