Locally hulled topologies
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866917813808005120 |
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| author | Bilokopytov, Eugene |
| author_facet | Bilokopytov, Eugene |
| contents | We present a general result about generating group topologies by pseudo-norms. Namely, we show that if a topology has a base of sets which are closed in a certain sense, then it can be generated by a collection of pseudo-norms such that the balls in these pseudo-norms are also closed in the same sense. The examples include linear and locally convex topologies on vector spaces, locally solid and Fatou topologies on vector lattices and Fréchet-Nikodým topologies on Boolean algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Locally hulled topologies Bilokopytov, Eugene Functional Analysis General Topology 22A20, 46A40, 52A01 We present a general result about generating group topologies by pseudo-norms. Namely, we show that if a topology has a base of sets which are closed in a certain sense, then it can be generated by a collection of pseudo-norms such that the balls in these pseudo-norms are also closed in the same sense. The examples include linear and locally convex topologies on vector spaces, locally solid and Fatou topologies on vector lattices and Fréchet-Nikodým topologies on Boolean algebras. |
| title | Locally hulled topologies |
| topic | Functional Analysis General Topology 22A20, 46A40, 52A01 |
| url | https://arxiv.org/abs/2410.18509 |