References
Tukia P. andVäisälä J., “Quasisymmetric embeddings of metric spaces,” Ann. Acad. Sci. Fenn. Ser. A1 Math.,5, No. 1, 97–114 (1980).
Aseev V. V. andKuzin D. G., “Sufficient conditions for quasisymmetry of mappings of the real axis and the plane,” Sibirsk. Mat. Zh.,39, No. 6, 1225–1235 (1998).
Tukia P, “Spaces and arcs of bounded turning,” Michigan Math. J.,43, No. 3, 559–584 (1996).
Kuzin D. G., “On criteria for quasisymmetry of a mapping from a straight line to the plane”, in: Proceedings of 34 International Student Research Conference. Mathematics [in Russian], Novosibirsk. Univ., Novosibirsk, 1996, pp. 43–44.
Aseev V. V., “Infinitesimally Jordan continua,” in: Abstracts: The Third Siberian Congress on Applied and Industrial mathematics Dedicated to the Memory of S. L. Sobolev, Sobolev Inst. Mat. (Novosibirsk), Novosibirsk, 1998, Part 1, pp. 55–56.
Kuratowski K., Topology. Vol. 1 and 2 [Russian translation], Mir, Moscow (1966, 1969).
Aleksandryan Z. A. andMirzakhanyan È. A., General Topology [in Russian], Vysshaya Shkola, Moscow (1979).
Hausdorff F., Set Theory [Russian translation], ONTI NKTP SSSR, Moscow (1937).
Zorich V. A., “On some open problems of the theory of quasiconformal space mappings,” in: Metric Problems of the Theory of Functions and Mappings [in Russian], Naukova Dumka, Kiev, 1971, No. 3, pp. 46–50.
Thurston W. P., “Zippers and univalent functions”, in: The Bieberbach Conjecture: Proc. of the Sympos. on the Occasion of the Proof (Math. Surveys and Monogr.,21), Amer. Math. Soc. 185–197 (1986).
Engelking R., General Topology [Russian translation], Mir, Moscow (1986).
Väisälä J., “Quasimöbius maps,” J. Analyse Math.,44, 218–234 (1984/1985).
Asseev V. V. andTrotsenko D. A., “Quasisymmetric embeddings, quadruples of points and distortions of moduli,” Sibirsk. Mat. Zh.,28, No. 4, 32–28 (1987).
Aseev V. V., “Quasisymmetric embeddings and mappings with bounded modulus distortion”, submitted to VINITI on November 6, 1994, No. 7190-84.
Aseev V. V., “Normal families of topological embeddings,” Dinamika Sploshn. Sredy (Novosibirsk), No. 76, 32–42 (1986).
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Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 41, No. 5, pp. 984–996, September–October, 2000.
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Aseev, V.V., Kuzin, D.G. Continua of bounded turning: Chain condition and infinitesimal connectedness. Sib Math J 41, 801–810 (2000). https://doi.org/10.1007/BF02674738
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DOI: https://doi.org/10.1007/BF02674738