Abstract
We study the mappings of metric spaces that distort the moduli of the families of paths according to the Poletsky inequality. In the case where the mapped domain is a weakly flat space, and the enveloping metric space admits a weak sphericalization, the equicontinuity of the corresponding families of inverse mappings is established. Under some additional conditions, the equicontinuity of the corresponding families of mappings in the closure of their domain of definition has proved.
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The paper is dedicated to the 100th anniversary of G. D. Suvorov
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 2, pp. 215–227 April–June, 2019.
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Sevost’yanov, E.A., Skvortsov, S.A. On the local behavior of mappings of metric spaces. J Math Sci 244, 47–55 (2020). https://doi.org/10.1007/s10958-019-04603-4
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DOI: https://doi.org/10.1007/s10958-019-04603-4