Concrete functors that respect initiality and finality
We study concrete endofunctors of the category of convergence spaces and continuous maps that send initial maps to initial maps or final maps to final maps. The former phenomenon turns out to be fairly common while the latter is rare. In particular, it is shown that the pretopological modification i...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2023-04-01
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| Series: | Applied General Topology |
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| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/18771 |
| _version_ | 1797851647959891968 |
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| author | Frédéric Mynard |
| author_facet | Frédéric Mynard |
| author_sort | Frédéric Mynard |
| collection | DOAJ |
| description | We study concrete endofunctors of the category of convergence spaces and continuous maps that send initial maps to initial maps or final maps to final maps. The former phenomenon turns out to be fairly common while the latter is rare. In particular, it is shown that the pretopological modification is the coarsest hereditary modifier finer than the topological modifier and this is applied to give a structural interpretation of the role of Fréchet-Urysohn spaces with respect to sequential spaces and of k' -spaces with respect to k -spaces. |
| first_indexed | 2024-04-09T19:21:09Z |
| format | Article |
| id | doaj.art-625dcabfe4f44cae92f2f9f1f34a7286 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-09T19:21:09Z |
| publishDate | 2023-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-625dcabfe4f44cae92f2f9f1f34a72862023-04-05T11:41:08ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472023-04-0124118720310.4995/agt.2023.1877117961Concrete functors that respect initiality and finalityFrédéric Mynard0https://orcid.org/0000-0002-1018-6748New Jersey City University, USAWe study concrete endofunctors of the category of convergence spaces and continuous maps that send initial maps to initial maps or final maps to final maps. The former phenomenon turns out to be fairly common while the latter is rare. In particular, it is shown that the pretopological modification is the coarsest hereditary modifier finer than the topological modifier and this is applied to give a structural interpretation of the role of Fréchet-Urysohn spaces with respect to sequential spaces and of k' -spaces with respect to k -spaces.https://polipapers.upv.es/index.php/AGT/article/view/18771convergence spaceheredityconcrete functors preserves initialitypre-serves finality |
| spellingShingle | Frédéric Mynard Concrete functors that respect initiality and finality Applied General Topology convergence space heredity concrete functors preserves initiality pre-serves finality |
| title | Concrete functors that respect initiality and finality |
| title_full | Concrete functors that respect initiality and finality |
| title_fullStr | Concrete functors that respect initiality and finality |
| title_full_unstemmed | Concrete functors that respect initiality and finality |
| title_short | Concrete functors that respect initiality and finality |
| title_sort | concrete functors that respect initiality and finality |
| topic | convergence space heredity concrete functors preserves initiality pre-serves finality |
| url | https://polipapers.upv.es/index.php/AGT/article/view/18771 |
| work_keys_str_mv | AT fredericmynard concretefunctorsthatrespectinitialityandfinality |