Bornological quasi-metrizability in generalized topology

Year 2019, Volume: 48 Issue: 6, 1653 - 1666, 08.12.2019

Artur Piękosz Eliza Wajch

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 ZF. An example of a weakly locally small space which is not locally small is constructed under ZF+CC. Several categories, relevant to generalized bornological universes, are defined and shown to be topological constructs.

Keywords

Delfs-Knebusch generalized topological space, quasi-metric, bornology, topological category, ZF

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