We study the problem of local behavior of maps in the closure of a domain in the Euclidean space. The equicontinuity of families of these map**s is established in the case where the mapped domain is not fixed. We separately consider the domains with bad and good boundaries, as well as the homeomorphisms and maps with branching.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 7, pp. 938–951, July, 2019.
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Sevost’yanov, E.A., Skvortsov, S.A. On the Equicontinuity of Families of Map**s in the Case of Variable Domains. Ukr Math J 71, 1071–1086 (2019). https://doi.org/10.1007/s11253-019-01699-4
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DOI: https://doi.org/10.1007/s11253-019-01699-4