Involutive quantales and quantale-enriched involutive topological spaces
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915487304122368 |
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| author | García, Javier Gutiérrez Höhle, Ulrich |
| author_facet | García, Javier Gutiérrez Höhle, Ulrich |
| contents | In this paper, we provide a comprehensive analysis of involutive quantales, with a particular focus on quantic frames. We extend the axiomatic foundations of quantale-enriched topological spaces to include closure under the anti-homomorphic involution, facilitating a balanced topologization of the spectrum of unital $C^*$-algebras that encompasses both closed right and left ideals through the concept of quantic frames. Specifically, certain subspaces of pure states are identified as strongly Hausdorff separated quantale-enriched involutive topological spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Involutive quantales and quantale-enriched involutive topological spaces García, Javier Gutiérrez Höhle, Ulrich Operator Algebras General Topology Primary 18F75 Secondary 06F07, 18D20 In this paper, we provide a comprehensive analysis of involutive quantales, with a particular focus on quantic frames. We extend the axiomatic foundations of quantale-enriched topological spaces to include closure under the anti-homomorphic involution, facilitating a balanced topologization of the spectrum of unital $C^*$-algebras that encompasses both closed right and left ideals through the concept of quantic frames. Specifically, certain subspaces of pure states are identified as strongly Hausdorff separated quantale-enriched involutive topological spaces. |
| title | Involutive quantales and quantale-enriched involutive topological spaces |
| topic | Operator Algebras General Topology Primary 18F75 Secondary 06F07, 18D20 |
| url | https://arxiv.org/abs/2503.03498 |