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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2209.14005 |
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| _version_ | 1866914971883929600 |
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| author | Goubault-Larrecq, Jean Jia, Xiaodong |
| author_facet | Goubault-Larrecq, Jean Jia, Xiaodong |
| contents | We show that every continuous valuation on a locally convex, locally convex-compact, sober topological cone $\mathfrak{C}$ has a barycenter. This barycenter is unique, and the barycenter map $β$ is continuous, hence is the structure map of a $\mathbf V_{\mathrm w}$-algebra, i.e., an Eilenberg-Moore algebra of the extended valuation monad on the category of $T_0$ topological spaces; it is, in fact, the unique $\mathbf V_{\mathrm w}$-algebra that induces the cone structure on $\mathfrak{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14005 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A cone-theoretic barycenter existence theorem Goubault-Larrecq, Jean Jia, Xiaodong General Topology We show that every continuous valuation on a locally convex, locally convex-compact, sober topological cone $\mathfrak{C}$ has a barycenter. This barycenter is unique, and the barycenter map $β$ is continuous, hence is the structure map of a $\mathbf V_{\mathrm w}$-algebra, i.e., an Eilenberg-Moore algebra of the extended valuation monad on the category of $T_0$ topological spaces; it is, in fact, the unique $\mathbf V_{\mathrm w}$-algebra that induces the cone structure on $\mathfrak{C}$. |
| title | A cone-theoretic barycenter existence theorem |
| topic | General Topology |
| url | https://arxiv.org/abs/2209.14005 |