The structure of extended real-valued quasi-metric spaces
dc.contributor.author | Matindih, Levy Kahyata | |
dc.date.accessioned | 2020-12-08T07:57:20Z | |
dc.date.available | 2020-12-08T07:57:20Z | |
dc.date.issued | 2018 | |
dc.description | Thesis | en |
dc.description.abstract | An extended quasi-metric q on a nonempty set X without any assumed structure is a distance functional that satis es the usual properties of a quasi-metric except that it can assume values of in nity, in addition to non-negative real values. Given a quasi-metrizable space X we exhibit a universal space for all extended quasi-metric spaces compatible with the asymmetric topologies of X. De ning a set in an extended quasi-metric space (X; q) to be bounded if it is contained in an intersection of the left-q and right-q open (or closed)-balls, we characterize these kinds of bornologies on X and, obtain necessary and su cient conditions in order for the same bornologies to be realized as those for quasi-metrically bounded sets. We also consider in this setting a second possible de nition of bounded sets involving quasicomponents. Keywords: Quasi-metric, Extended real-valued quasi-metric, uniform equivalent quasimetrics, Bounded set, Partial function, Bornology, Quasi-metric bornology, Quasi isometry, Free union bitopology, Generalized Hus Theorem. | en |
dc.identifier.uri | http://dspace.unza.zm/handle/123456789/6701 | |
dc.language.iso | en | en |
dc.publisher | The University of Zambia | en |
dc.subject | Quasi-metric--Zambia | en |
dc.subject | Quasi isometry | en |
dc.title | The structure of extended real-valued quasi-metric spaces | en |
dc.type | Thesis | en |