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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Carathéodory distance does not define the topology


Author: Jean-Pierre Vigué
Journal: Proc. Amer. Math. Soc. 91 (1984), 223-224
MSC: Primary 32H15
MathSciNet review: 740175
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Abstract: We construct an analytic space $ X$ such that the Carathéodory pseudo-distance $ {c_X}$ is a true distance on $ X$; however, $ {c_X}$ does not define the analytic space topology of $ X$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740175-9
PII: S 0002-9939(1984)0740175-9
Keywords: Carathéodory distance, topology defined by the Caratheodory distance
Article copyright: © Copyright 1984 American Mathematical Society