Remarks on a result of Sibony on the Carathéodory topology
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911300539383808 |
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| author | Dolai, Sudip |
| author_facet | Dolai, Sudip |
| contents | In this paper, we prove that if a Carathéodory hyperbolic analytic space $X$ is $C_X$-complete, then its natural topology is induced by the Carathéodory distance on $X$. This is an improvement of Sibony's result, which concludes the same under the hypothesis that $X$ is $C_X$-finitely compact. This improvement is not merely formal; we also show the existence of uncountably many biholomorphically inequivalent analytic spaces that are not $C_X$-finitely compact but are $C_X$-complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on a result of Sibony on the Carathéodory topology Dolai, Sudip Complex Variables Metric Geometry 32C18, 32F45, 51F99 (Primary) 30C20, 30L15 (Secondary) In this paper, we prove that if a Carathéodory hyperbolic analytic space $X$ is $C_X$-complete, then its natural topology is induced by the Carathéodory distance on $X$. This is an improvement of Sibony's result, which concludes the same under the hypothesis that $X$ is $C_X$-finitely compact. This improvement is not merely formal; we also show the existence of uncountably many biholomorphically inequivalent analytic spaces that are not $C_X$-finitely compact but are $C_X$-complete. |
| title | Remarks on a result of Sibony on the Carathéodory topology |
| topic | Complex Variables Metric Geometry 32C18, 32F45, 51F99 (Primary) 30C20, 30L15 (Secondary) |
| url | https://arxiv.org/abs/2512.03901 |