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arXiv · 2512.03901

Remarks on a result of Sibony on the Carath\'eodory topology

Sudip Dolai
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Abstract

In this paper, we prove that if a Carath\'eodory hyperbolic analytic space $X$ is $C_X$-complete, then its natural topology is induced by the Carath\'eodory 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.

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Sudip Dolai. 2025-12-03. Remarks on a result of Sibony on the Carath\'eodory topology. https://arxiv.org/abs/2512.03901

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