Functorial approach structures
We show that there exists at least a proper class of functorial approach structures, i.e., right inverses to the forgetful functor T : AP→ Top (where AP denotes the topological construct of approach spaces and contractions as introduced by R. Lowen). There is however a great difference in nature of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2003-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/2012 |
| _version_ | 1819086225477206016 |
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| author | Guillaume C.L. Brümmer Mark Sioen |
| author_facet | Guillaume C.L. Brümmer Mark Sioen |
| author_sort | Guillaume C.L. Brümmer |
| collection | DOAJ |
| description | We show that there exists at least a proper class of functorial approach structures, i.e., right inverses to the forgetful functor T : AP→ Top (where AP denotes the topological construct of approach spaces and contractions as introduced by R. Lowen). There is however a great difference in nature of these functorial approach structures when compared to the quasi-uniform paradigm which has been extensively studied by the first author: whereas it is well-known from [2] that a large class of epireflective subcategories of Top0 can be “parametrized” using the interaction of functorial quasi-uniformities with the quasi-uniform bicompletion, we show that using functorial approach structures together with the approach bicompletion developed in [10], only Top0 itself can be retrieved in this way. |
| first_indexed | 2024-12-21T21:16:52Z |
| format | Article |
| id | doaj.art-9f5f79a493014bf6b7bccfa5b9269571 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-21T21:16:52Z |
| publishDate | 2003-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-9f5f79a493014bf6b7bccfa5b92695712022-12-21T18:49:59ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472003-04-0141919710.4995/agt.2003.20121633Functorial approach structuresGuillaume C.L. Brümmer0Mark Sioen1University of Cape TownFree University of BrusselsWe show that there exists at least a proper class of functorial approach structures, i.e., right inverses to the forgetful functor T : AP→ Top (where AP denotes the topological construct of approach spaces and contractions as introduced by R. Lowen). There is however a great difference in nature of these functorial approach structures when compared to the quasi-uniform paradigm which has been extensively studied by the first author: whereas it is well-known from [2] that a large class of epireflective subcategories of Top0 can be “parametrized” using the interaction of functorial quasi-uniformities with the quasi-uniform bicompletion, we show that using functorial approach structures together with the approach bicompletion developed in [10], only Top0 itself can be retrieved in this way.http://polipapers.upv.es/index.php/AGT/article/view/2012Approach space(approach) bicompletenessEpireflective subcategoryFunctorial approach structureSpanningTopological space |
| spellingShingle | Guillaume C.L. Brümmer Mark Sioen Functorial approach structures Applied General Topology Approach space (approach) bicompleteness Epireflective subcategory Functorial approach structure Spanning Topological space |
| title | Functorial approach structures |
| title_full | Functorial approach structures |
| title_fullStr | Functorial approach structures |
| title_full_unstemmed | Functorial approach structures |
| title_short | Functorial approach structures |
| title_sort | functorial approach structures |
| topic | Approach space (approach) bicompleteness Epireflective subcategory Functorial approach structure Spanning Topological space |
| url | http://polipapers.upv.es/index.php/AGT/article/view/2012 |
| work_keys_str_mv | AT guillaumeclbrummer functorialapproachstructures AT marksioen functorialapproachstructures |