On complete spaces for the Carathéodory distance

Larbi Belkhchicha; Jean-Pierre Vigué

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 2, page 189-192
  • ISSN: 1120-6330

Abstract

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An example of a finite dimensional analytic space is exhibited, for which the Carathéodory integrated distance and the Carathéodory distance, although defining the same topology, are respectively complete and incomplete.

How to cite

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Belkhchicha, Larbi, and Vigué, Jean-Pierre. "Sur les espaces complets pour la distance de Carathéodory." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.2 (1994): 189-192. <http://eudml.org/doc/244155>.

@article{Belkhchicha1994,
author = {Belkhchicha, Larbi, Vigué, Jean-Pierre},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Carathéodory distance; Carathéodory integrated distance; Analytic space; inner Carathéodory distance},
language = {fre},
month = {6},
number = {2},
pages = {189-192},
publisher = {Accademia Nazionale dei Lincei},
title = {Sur les espaces complets pour la distance de Carathéodory},
url = {http://eudml.org/doc/244155},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Belkhchicha, Larbi
AU - Vigué, Jean-Pierre
TI - Sur les espaces complets pour la distance de Carathéodory
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/6//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 2
SP - 189
EP - 192
LA - fre
KW - Carathéodory distance; Carathéodory integrated distance; Analytic space; inner Carathéodory distance
UR - http://eudml.org/doc/244155
ER -

References

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  1. DINEEN, S., The Schwarz Lemma. Clarendon Press, Oxford1989. Zbl0708.46046MR1033739
  2. FRANZONI, T. - VESENTINI, E., Holomorphic Maps and Invariant Distances. North-Holland Math. Studies, 40, Amsterdam1980.. Zbl0447.46040MR563329
  3. JARNICKI, M. - PFLUG, P. - VIGUE, J. P., The Carathéodory distance does not define the topology - the case of domains. C. R. Acad. Sc. Paris, Série I, 312, 1991, 77-79. Zbl0721.32010MR1086505
  4. JARNICKI, M. - PFLUG, P. - VIGUÉ, J.-P., An example of a Carathéodory complete but not finitely compact analytic space. Proc. A.M.S., 118, 1993, 537-539. Zbl0780.32003MR1148025DOI10.2307/2160335
  5. KOBAYASHI, S., Intrinsic distances, measures and geometric function theory. Bull. A.M.S., 82, 1976, 357-416. Zbl0346.32031MR414940
  6. RINOW, W., Die innere Geometrie der metrischen Räume. Die Grundlehren der Math. Wissenschaften, Band 105, Springer-Verlag, Berlin1961. Zbl0096.16302MR123969

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