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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/2601.10840 |
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| _version_ | 1866918291747897344 |
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| author | Craig, Andrew Haviar, Miroslav |
| author_facet | Craig, Andrew Haviar, Miroslav |
| contents | We describe digraphs with topology which give dual representations of ortholattices. This is done via so-called dual Ploščica spaces of lattices. First, we improve the definition of Ploščica spaces from an earlier paper to give a straight and natural generalisation of the total order disconnectedness of Priestley spaces. Then we define the dual space of a general ortholattice as the dual Ploščica space of the lattice-reduct of the ortholattice equipped with a map representing the orthocomplement operation. We introduce an abstract ortho-Ploščica space capturing the properties of the dual space of an ortholattice, and we present dual representation theorems between general ortholattices and the ortho-Ploščica spaces. We illustrate our dual representations by examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10840 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dual Ploščica spaces of ortholattices Craig, Andrew Haviar, Miroslav Rings and Algebras Logic We describe digraphs with topology which give dual representations of ortholattices. This is done via so-called dual Ploščica spaces of lattices. First, we improve the definition of Ploščica spaces from an earlier paper to give a straight and natural generalisation of the total order disconnectedness of Priestley spaces. Then we define the dual space of a general ortholattice as the dual Ploščica space of the lattice-reduct of the ortholattice equipped with a map representing the orthocomplement operation. We introduce an abstract ortho-Ploščica space capturing the properties of the dual space of an ortholattice, and we present dual representation theorems between general ortholattices and the ortho-Ploščica spaces. We illustrate our dual representations by examples. |
| title | Dual Ploščica spaces of ortholattices |
| topic | Rings and Algebras Logic |
| url | https://arxiv.org/abs/2601.10840 |