Bornological quasi-metrizability in generalized topology
arXiv:1505.04442 · doi:10.15672/HJMS.2018.596
Abstract
A concept of quasi-metrizability with respect to a bornology of a generalized topological space in the sense of Delfs and Knebusch is introduced. Quasi-metrization theorems for generalized bornological universes are deduced. A uniform quasi-metrizability with respect to a bornology is studied. The class of locally small spaces is considered and a possibly larger class of weakly locally small spaces is defined. The proofs and numerous examples are given in \textbf{ZF}. An example of a weakly locally small space which is not locally small is constructed under \textbf{ZF+CC}. Several categories, relevant to generalized bornological universes, are defined and shown to be topological constructs.
Submitted and accepted to Hacettepe Journal of Mathematics and Statistics. arXiv admin note: substantial text overlap with arXiv:1408.4823