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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.00194 |
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| _version_ | 1866915904218988544 |
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| author | Ortiz, Marby Zuley Bolaños De La Pava, Luz Victoria Russo, Ciro |
| author_facet | Ortiz, Marby Zuley Bolaños De La Pava, Luz Victoria Russo, Ciro |
| contents | We propose a point-free approach to MV-topological spaces in the wake of previous works on both classical and fuzzy topology. In order to do that, we introduce suitable frame-type structures and a class of fuzzy topological spaces which includes and suitably extends the one of MV-topological spaces. Then we show an adjoint situation between such structures, and restrict such an adjointness to a duality between the corresponding classes of ``spatial frames'' and ``sober spaces''. We also use neighbourhood systems to characterize sobriety in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Point-free MV-topologies Ortiz, Marby Zuley Bolaños De La Pava, Luz Victoria Russo, Ciro Logic We propose a point-free approach to MV-topological spaces in the wake of previous works on both classical and fuzzy topology. In order to do that, we introduce suitable frame-type structures and a class of fuzzy topological spaces which includes and suitably extends the one of MV-topological spaces. Then we show an adjoint situation between such structures, and restrict such an adjointness to a duality between the corresponding classes of ``spatial frames'' and ``sober spaces''. We also use neighbourhood systems to characterize sobriety in this context. |
| title | Point-free MV-topologies |
| topic | Logic |
| url | https://arxiv.org/abs/2604.00194 |