Integer-valued valuations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866915745061928960 |
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| author | Ilienko, Andrii Molchanov, Ilya Visonà, Tommaso |
| author_facet | Ilienko, Andrii Molchanov, Ilya Visonà, Tommaso |
| contents | We obtain a complete characterization of planar monotone $σ$-continuous valuations taking integer values, without assuming invariance under any group of transformations. We further investigate the consequences of dropping monotonicity or $σ$-continuity and give a full classification of line valuations. We also introduce a construction of the product for valuations of this type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21144 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integer-valued valuations Ilienko, Andrii Molchanov, Ilya Visonà, Tommaso Metric Geometry 52A10 We obtain a complete characterization of planar monotone $σ$-continuous valuations taking integer values, without assuming invariance under any group of transformations. We further investigate the consequences of dropping monotonicity or $σ$-continuity and give a full classification of line valuations. We also introduce a construction of the product for valuations of this type. |
| title | Integer-valued valuations |
| topic | Metric Geometry 52A10 |
| url | https://arxiv.org/abs/2502.21144 |