Implicative-ortholattices as orthogonality spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908751550742528 |
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| author | Ciungu, Lavinia Corina |
| author_facet | Ciungu, Lavinia Corina |
| contents | We obtain an orthogonality space by endowing an implicative-ortholattice with a suitable orthogonality relation; for such spaces, we also investigate the particular case of implicative-orthomodular lattices. Moreover, we define the commutativity relation between two elements of an implicative-ortholattice, as well as the Sasaki projections on this structure. Furthermore, we characterize the implicative-orthomodular lattices and implicative-Boolean algebras, showing that the center of an implicative-orthomodular lattice is an implicative-Boolean algebra. We prove that an implicative-ortholattice is an implicative-orthomodular lattice if and only if it admits a full Sasaki set of projections. Finally, based on Sasaki maps on implicative-ortholattices, we introduce the notion of Sasaki spaces, proving that when a complete implicative-ortholattice admits a full Sasaki set of projections, it is a Sasaki space. We also provide a characterization of Dacey spaces arising from implicative-ortholattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01848 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Implicative-ortholattices as orthogonality spaces Ciungu, Lavinia Corina General Mathematics We obtain an orthogonality space by endowing an implicative-ortholattice with a suitable orthogonality relation; for such spaces, we also investigate the particular case of implicative-orthomodular lattices. Moreover, we define the commutativity relation between two elements of an implicative-ortholattice, as well as the Sasaki projections on this structure. Furthermore, we characterize the implicative-orthomodular lattices and implicative-Boolean algebras, showing that the center of an implicative-orthomodular lattice is an implicative-Boolean algebra. We prove that an implicative-ortholattice is an implicative-orthomodular lattice if and only if it admits a full Sasaki set of projections. Finally, based on Sasaki maps on implicative-ortholattices, we introduce the notion of Sasaki spaces, proving that when a complete implicative-ortholattice admits a full Sasaki set of projections, it is a Sasaki space. We also provide a characterization of Dacey spaces arising from implicative-ortholattices. |
| title | Implicative-ortholattices as orthogonality spaces |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2503.01848 |