Topologies defined by some invariant pseudodistances
Banach Center Publications (1995)
- Volume: 31, Issue: 1, page 69-76
- ISSN: 0137-6934
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topBarth, Theodore. "Topologies defined by some invariant pseudodistances." Banach Center Publications 31.1 (1995): 69-76. <http://eudml.org/doc/262804>.
@article{Barth1995,
author = {Barth, Theodore},
journal = {Banach Center Publications},
keywords = {invariant pseudodistances; topology; complex spaces},
language = {eng},
number = {1},
pages = {69-76},
title = {Topologies defined by some invariant pseudodistances},
url = {http://eudml.org/doc/262804},
volume = {31},
year = {1995},
}
TY - JOUR
AU - Barth, Theodore
TI - Topologies defined by some invariant pseudodistances
JO - Banach Center Publications
PY - 1995
VL - 31
IS - 1
SP - 69
EP - 76
LA - eng
KW - invariant pseudodistances; topology; complex spaces
UR - http://eudml.org/doc/262804
ER -
References
top- [AnS] A. Andreotti and W. Stoll, Extension of holomorphic maps, Ann. of Math. (2) 72 (1960), 312-349 Zbl0095.28101
- [Au] V. Aurich, Bounded analytic sets in Banach spaces, Ann. Inst. Fourier (Grenoble) 36 (1986), 229-243 Zbl0591.46005
- [B72] T. J. Barth, The Kobayashi distance induces the standard topology, Proc. Amer. Math. Soc. 35 (1972), 439-441 Zbl0259.32007
- [B77] T. J. Barth, Some counterexamples concerning intrinsic distances, Proc. Amer. Math. Soc. 66 (1977), 49-53 Zbl0331.32019
- [C] C. Carathéodory, Über das Schwarzsche Lemma bei analytischen Funktionen von zwei komplexen Veränderlichen, Math. Ann. 97 (1926), 76-98 Zbl52.0345.02
- [Di] S. Dineen, The Schwarz Lemma Oxford University Press, 1989.
- [DiT] S. Dineen and R. M. Timoney, Complex geodesics on convex domains, in: Progress in Functional Analysis, North-Holland 1992, 333-365 Zbl0785.46044
- [DiTV] S. Dineen, R. M. Timoney et J.-P. Vigué, Pseudodistances invariantes sur les domaines d'un espace localement convexe, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 12 (1985), 515-529 Zbl0603.46052
- [Do] A. Douady, A remark on Banach analytic spaces, in: Symposium on Infinite Dimensional Topology, Princeton University Press 1972, 41-42
- [EaH] C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings in: Global Analysis (Berkeley, Calif. 1968), Proc. Sympos. Pure Math. 16,, Amer. Math. Soc. 1970, 61-65
- [ElG] Y. Eliashberg and M. Gromov, Embeddings of Stein manifolds of dimension n into the affine space of dimension 3n/2+1, Ann. of Math. (2) 136 (1992), 123-135 Zbl0758.32012
- [FS77] J. E. Fornaess and E. L. Stout, Spreading polydiscs on complex manifolds, Amer. J. Math. 99 (1977), 933-960 Zbl0384.32004
- [FS82] J. E. Fornaess and E. L. Stout, J. E. Fornaess, E. L. Stout, Regular holomorphic images of balls, Ann. Inst. Fourier (Grenoble) 32 (1982), 23-36 Zbl0452.32008
- [FV] T. Franzoni and E. Vesentini, Holomorphic Maps and Invariant Distances, North-Holland 1980. Zbl0447.46040
- [G] R. C. Gunning, On Vitali's theorem for complex spaces with singularities, J. Math. Mech. 8 (1959), 133-141 Zbl0092.07503
- [GR] R. C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall 1965. Zbl0141.08601
- [Ha] M. Hayashi, The maximal ideal space of the bounded analytic functions on a Riemann surface, J. Math. Soc. Japan 39 (1987), 337-344 Zbl0598.30070
- [He] M. Hervé, Analyticity in Infinite Dimensional Spaces, Walter de Gruyter 1989. Zbl0666.58008
- [Hi] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math. (2) 79 (1964), 109-326 Zbl0122.38603
- [HiR] H. Hironaka and H. Rossi, On the equivalence of imbeddings of exceptional complex spaces, Math. Ann. 156 (1964), 313-333 Zbl0136.20801
- [JP90] M. Jarnicki and P. Pflug, The simplest example for the non-innerness of the Carathéodory distance, Results Math. 18 (1990), 57-59 Zbl0709.32015
- [JP91] M. Jarnicki and P. Pflug, M. Jarnicki, P. Pflug, Invariant pseudodistances and pseudometrics-completeness and the product property, Ann. Polon. Math. 55 (1991), 169-189 Zbl0756.32016
- [JPV91] M. Jarnicki, P. Pflug and J.-P. Vigué, The Carathéodory distance does not define the topology-the case of domains, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), 77-79 Zbl0721.32010
- [JPV92] M. Jarnicki, M. Jarnicki, P. Pflug, J.-P. Vigué, A remark on Carathéodory balls, Arch. Math. (Basel) 58 (1992), 595-598
- [K67] S. Kobayashi, Invariant distances on complex manifolds and holomorphic mappings, J. Math. Soc. Japan 19 (1967), 460-480 Zbl0158.33201
- [K70] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker 1970.
- [K73] S. Kobayashi, Some remarks and questions concerning the intrinsic distance, Tôhoku Math. J. (2) 25 (1973), 481-486 Zbl0281.32017
- [K76] S. Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc. 82 (1976), 357-416 Zbl0346.32031
- [K90] S. Kobayashi, A new invariant infinitesimal metric, Internat. J. Math. 1 (1990), 83-90 Zbl0702.32021
- [La] S. Lang, Introduction to Complex Hyperbolic Spaces, Springer 1987. Zbl0628.32001
- [Le] J. Lewittes, A note on parts and hyperbolic geometry, Proc. Amer. Math. Soc. 17 (1966), 1087-1090 Zbl0196.13801
- [Lo] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser 1991.
- [M] K. Menger, Untersuchungen über allgemeine Metrik. IV. Zur Metrik der Kurven, Math. Ann. 103 (1930), 466-501 Zbl56.0508.04
- [PS] E. A. Poletskiĭ and B. V. Shabat, Invariant metrics in: Complex Analysis-Several Variables 3, VINITI, Moscow, 1986 (in Russian); English transl.: Several Complex Variables III, Encyclopaedia Math. Sci. 9, Springer, 1989, 63-111
- [Re] H.-J. Reiffen, Die Carathéodorysche Distanz und ihre zugehörige Differentialmetrik, Math. Ann. 161 (1965), 315-324 Zbl0141.08803
- [Ri] W. Rinow, Die innere Geometrie der metrischen Räume, Springer 1961. Zbl0096.16302
- [Ro] H. L. Royden, Remarks on the Kobayashi metric in: Several Complex Variables II Maryland 1970, Lecture Notes in Math. 185,, Springer 1971, 125-137.
- [Sib] N. Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230 Zbl0333.32011
- [Siu] Y. T. Siu, Every Stein subvariety admits a Stein neighborhood ibid. 38 (1976), 89-100 Zbl0343.32014
- [Ve] S. Venturini, Pseudodistances and pseudometrics on real and complex manifolds, Ann. Mat. Pura Appl. (4) 154 (1989), 385-402 Zbl0702.32022
- [Vi83] J.-P. Vigué, La distance de Carathéodory n'est pas intérieure, Results Math. 6 (1983), 100-104 Zbl0552.32022
- [Vi84] J.-P. Vigué, The Carathéodory distance does not define the topology, Proc. Amer. Math. Soc. 91 (1984), 223-224 Zbl0555.32016
- [W] H. Wu, Normal families of holomorphic mappings, Acta Math. 119 (1967), 193-233 Zbl0158.33301
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