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The Kobayashi distance induces the standard topology


Author: Theodore J. Barth
Journal: Proc. Amer. Math. Soc. 35 (1972), 439-441
MSC: Primary 32C15
DOI: https://doi.org/10.1090/S0002-9939-1972-0306545-X
MathSciNet review: 0306545
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Abstract: The Kobayashi pseudodistance on a connected complex space is continuous with respect to the standard topology. If this pseudodistance is an actual distance, it induces the standard topology.


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  • [1] D. A. Eisenman, Intrinsic measures on complex manifolds and holomorphic mappings, Mem. Amer. Math. Soc. No. 96 (1970). MR 41 #3807. MR 0259165 (41:3807)
  • [2] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109-326. MR 33 #7333. MR 0199184 (33:7333)
  • [3] H. Hironaka and H. Rossi, On the equivalence of imbeddings of exceptional complex spaces, Math. Ann. 156 (1964), 313-333. MR 30 #2011. MR 0171784 (30:2011)
  • [4] P. Kiernan, On the relations between taut, tight, and hyperbolic manifolds, Bull. Amer. Math. Soc. 76 (1970), 49-51. MR 40 #5896. MR 0252678 (40:5896)
  • [5] -, Some results concerning hyperbolic manifolds, Proc. Amer. Math. Soc. 25 (1970), 588-592. MR 41 #2044. MR 0257393 (41:2044)
  • [6] S. Kobayashi, Invariant distances on complex manifolds and holomorphic mappings, J. Math. Soc. Japan 19 (1967), 460-480. MR 38 #736. MR 0232411 (38:736)
  • [7] -, Hyperbolic manifolds and holomorphic mappings, Marcel Dekker, New York, 1970. MR 0277770 (43:3503)
  • [8] M. H. Kwack, Generalization of the big Picard theorem, Ann. of Math. (2) 90 (1969), 9-22. MR 39 #4445. MR 0243121 (39:4445)
  • [9] H. L. Royden, Remarks on the Kobayashi metric, Several Complex Variables. II (Maryland 1970), Lecture Notes in Math., no. 185, Springer-Verlag, Berlin and New York, 1971, pp. 125-137. MR 0304694 (46:3826)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0306545-X
Keywords: Kobayashi pseudodistance, Kobayashi distance, resolution of singularities
Article copyright: © Copyright 1972 American Mathematical Society

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