Metric spaces and textures
Textures are point-set setting for fuzzy sets, and they provide a framework for the complement-free mathematical concepts. Further dimetric on textures is a gener- alization of classical metric spaces. The aim of this paper is to give some properties of dimetric texture space by using categorical ap...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2017-04-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/6889 |
| _version_ | 1818484516541431808 |
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| author | Senol Dost |
| author_facet | Senol Dost |
| author_sort | Senol Dost |
| collection | DOAJ |
| description | Textures are point-set setting for fuzzy sets, and they provide a framework for the complement-free mathematical concepts. Further dimetric on textures is a gener- alization of classical metric spaces. The aim of this paper is to give some properties of dimetric texture space by using categorical approach. We prove that the category of clas- sical metric spaces is isomorphic to a full subcategory of dimetric texture spaces, and give a natural transformation from metric topologies to dimetric ditopologies. Further, it is pre- sented a relation between dimetric texture spaces and quasi-pseudo metric spaces in the sense of J. F. Kelly. |
| first_indexed | 2024-12-10T15:56:36Z |
| format | Article |
| id | doaj.art-ad6bd09cac0c4f1e97a2a87e4ae86a57 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-10T15:56:36Z |
| publishDate | 2017-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-ad6bd09cac0c4f1e97a2a87e4ae86a572022-12-22T01:42:37ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472017-04-0118120321710.4995/agt.2017.68895221Metric spaces and texturesSenol Dost0Hacettepe UniversityTextures are point-set setting for fuzzy sets, and they provide a framework for the complement-free mathematical concepts. Further dimetric on textures is a gener- alization of classical metric spaces. The aim of this paper is to give some properties of dimetric texture space by using categorical approach. We prove that the category of clas- sical metric spaces is isomorphic to a full subcategory of dimetric texture spaces, and give a natural transformation from metric topologies to dimetric ditopologies. Further, it is pre- sented a relation between dimetric texture spaces and quasi-pseudo metric spaces in the sense of J. F. Kelly.http://polipapers.upv.es/index.php/AGT/article/view/6889metric spacetexture spaceuniformitynatural transformationdifunctionisomorphism |
| spellingShingle | Senol Dost Metric spaces and textures Applied General Topology metric space texture space uniformity natural transformation difunction isomorphism |
| title | Metric spaces and textures |
| title_full | Metric spaces and textures |
| title_fullStr | Metric spaces and textures |
| title_full_unstemmed | Metric spaces and textures |
| title_short | Metric spaces and textures |
| title_sort | metric spaces and textures |
| topic | metric space texture space uniformity natural transformation difunction isomorphism |
| url | http://polipapers.upv.es/index.php/AGT/article/view/6889 |
| work_keys_str_mv | AT senoldost metricspacesandtextures |