Far Eastern Mathematical Journal

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Transfinite diameters and modulii of condensers in semimetric spaces

V. V. Aseev, O. A. Lazareva

2004, issue 1, P. 12–21

Abstract

The classical definitions for transfinite diameter of a set and for transfinite (discrete) modulus of a condenser in Rn have been extended for the objects in semimetric spaces. The Anderson-Vamanamurthy's folmula has been proved to be valid in arbitrary semimetric spaces. The Belinskij's problem on the Mobius property of topological embeddings, which are preserving transfinite modulii of all condensers of the given type, has been solved in the spaces with a continuous semimetric. Bibl. 12.

Keywords: semimetric space, semimetric, metric space, transfinite diameter, Robin constant, Mobius mappings, transfinite modulus of condenser, conformal modulus of condenser

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References

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