Countability conditions in locally solid convergence spaces
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915501620330496 |
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| author | Bilokopytov, Eugene Bohdanskyi, Viktor van der Walt, Jan Harm |
| author_facet | Bilokopytov, Eugene Bohdanskyi, Viktor van der Walt, Jan Harm |
| contents | We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively unform-, order-, and $σ$-order convergence, respectively, is (strongly) first countable. The implications for the validity of sequential arguments in the contexts of these convergences are pointed out. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Countability conditions in locally solid convergence spaces Bilokopytov, Eugene Bohdanskyi, Viktor van der Walt, Jan Harm Functional Analysis Primary: 46A19, 46A40. Secondary: 54D55 We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively unform-, order-, and $σ$-order convergence, respectively, is (strongly) first countable. The implications for the validity of sequential arguments in the contexts of these convergences are pointed out. |
| title | Countability conditions in locally solid convergence spaces |
| topic | Functional Analysis Primary: 46A19, 46A40. Secondary: 54D55 |
| url | https://arxiv.org/abs/2501.11517 |