
Journal of Convex Analysis 22 (2015), No. 4, 10411060 Copyright Heldermann Verlag 2015 QuasiMetrizability of Bornological Biuniverses in ZF Artur Piekosz Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31155 Cracow, Poland pupiekos@cyfronet.pl Eliza Wajch Institute of Mathematics and Physics, Siedlce University of Natural Sciences and Humanities, 3 Maja 54, 08110 Siedlce, Poland eliza.wajch@wp.pl Hu's metrization theorem for bornological universes is shown to hold in ZF and it is adapted to a quasimetrization theorem for bornologies in bitopological spaces. The problem of uniform quasimetrization of quasimetric bornological universes is investigated and several relevant results independent of ZF are obtained. In particular, some theorems of Garrido and Meroņo that contain necessary and sufficient conditions for a bornology in a metric space to be uniformly metrizable are generalized to quasimetric bornological universes in ZF, while some other theorems of Garrido and Meroņo are shown to fail in a model for ZF. Keywords: Bornology, bitopological space, quasimetric, ZF. MSC: 54E55, 54A35; 54E35, 54E99 [ Fulltextpdf (214 KB)] for subscribers only. 