Bornological quasi-metrizability in generalized topology
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.
Keywords
Cite
@article{arxiv.1505.04442,
title = {Bornological quasi-metrizability in generalized topology},
author = {Artur Piękosz and Eliza Wajch},
journal= {arXiv preprint arXiv:1505.04442},
year = {2018}
}
Comments
Submitted and accepted to Hacettepe Journal of Mathematics and Statistics. arXiv admin note: substantial text overlap with arXiv:1408.4823