Every finite system of T1 uniformities comes from a single distance structure

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dc.identifier.uri http://dx.doi.org/10.15488/5176
dc.identifier.uri https://www.repo.uni-hannover.de/handle/123456789/5223
dc.contributor.author Heitzig, Jobst
dc.date.accessioned 2019-08-15T09:06:59Z
dc.date.available 2019-08-15T09:06:59Z
dc.date.issued 2002
dc.identifier.citation Heitzig, Jobst: Every finite system of T1 uniformities comes from a single distance structure. In: Applied General Topology 3 (2002), Nr. 1, S. 65-76. DOI: https://doi.org/10.4995/agt.2002.2113
dc.description.abstract Using the general notion of distance function introduced in an earlier paper, a construction of the finest distance structure which induces a given quasi-uniformity is given. Moreover, when the usual defining condition xy : d(y; x) of the basic entourages is generalized to nd(y; x) n (for a fixed positive integer n), it turns out that if the value-monoid of the distance function is commutative, one gets a countably infinite family of quasi-uniformities on the underlying set. It is then shown that at least every finite system and every descending sequence of T1 quasi-uniformities which fulfil a weak symmetry condition is included in such a family. This is only possible since, in contrast to real metric spaces, the distance function need not be symmetric. eng
dc.language.iso eng
dc.publisher Valencia : Universitat Politecnica de Valencia
dc.relation.ispartofseries Applied General Topology 3 (2002), Nr. 1
dc.rights CC BY-NC-ND 4.0 Unported
dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject Countable set eng
dc.subject Minkowski distance eng
dc.subject Topology eng
dc.subject Free monoid eng
dc.subject Commutative property eng
dc.subject Metric space eng
dc.subject Metric (mathematics) eng
dc.subject Mathematics eng
dc.subject Integer eng
dc.subject.ddc 510 | Mathematik ger
dc.title Every finite system of T1 uniformities comes from a single distance structure
dc.type Article
dc.type Text
dc.relation.issn 1576-9402
dc.relation.doi https://doi.org/10.4995/agt.2002.2113
dc.bibliographicCitation.issue 1
dc.bibliographicCitation.volume 3
dc.bibliographicCitation.firstPage 65
dc.bibliographicCitation.lastPage 76
dc.description.version publishedVersion
tib.accessRights frei zug�nglich

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