2025/12/03 by Dolai, Sudip
#30L15 (Secondary) #32C18 #32F45 #51F99 (Primary) 30C20 #Complex Variables (math.CV) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2512.03901
In this paper, we prove that if a Carathéodory hyperbolic analytic space X is CX-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 CX-finitely compact. This improvement is not merely formal; we also show the existence of uncountably many biholomorphically inequivalent analytic spaces that are not CX-finitely compact but are CX-complete.