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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