Every finite system of T1 uniformities comes from a single distance structure
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| dc.contributor.author | Heitzig, Jobst
|
es_ES |
| dc.date.accessioned | 2017-05-30T10:50:47Z | |
| dc.date.available | 2017-05-30T10:50:47Z | |
| dc.date.issued | 2002-04-01 | |
| dc.identifier.issn | 1576-9402 | |
| dc.identifier.uri | http://hdl.handle.net/10251/82020 | |
| dc.description.abstract | [EN] 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. | es_ES |
| dc.language | Inglés | es_ES |
| dc.publisher | Universitat Politècnica de València | |
| dc.relation.ispartof | Applied General Topology | |
| dc.rights | Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) | es_ES |
| dc.subject | Distance function | es_ES |
| dc.subject | Free monoid | es_ES |
| dc.subject | Generalized metric | es_ES |
| dc.subject | Uniformity | es_ES |
| dc.title | Every finite system of T1 uniformities comes from a single distance structure | es_ES |
| dc.type | Artículo | es_ES |
| dc.date.updated | 2017-05-30T09:28:18Z | |
| dc.identifier.doi | 10.4995/agt.2002.2113 | |
| dc.rights.accessRights | Abierto | es_ES |
| dc.description.bibliographicCitation | Heitzig, J. (2002). Every finite system of T1 uniformities comes from a single distance structure. Applied General Topology. 3(1):65-76. https://doi.org/10.4995/agt.2002.2113 | es_ES |
| dc.description.accrualMethod | SWORD | es_ES |
| dc.relation.publisherversion | https://doi.org/10.4995/agt.2002.2113 | es_ES |
| dc.description.upvformatpinicio | 65 | es_ES |
| dc.description.upvformatpfin | 76 | es_ES |
| dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
| dc.description.volume | 3 | |
| dc.description.issue | 1 | |
| dc.identifier.eissn | 1989-4147 | |
| dc.provenance | Universitat Politècnica de València |
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