On the Equicontinuity of One Family of Inverse Mappings in Terms of Prime Ends
- 18 Downloads
For a class of mappings satisfying upper modular estimates with respect to the families of curves, we study the local behavior of the corresponding inverse mappings. In terms of prime ends, we prove that the families of these homeomorphisms are equicontinuous (normal) in the closure of a given domain.
Unable to display preview. Download preview PDF.
- 2.D. A. Kovtonyuk and V. I. Ryazanov, “On the theory of prime ends for space mappings,” Ukr. Mat. Zh., 67, No. 4, 467–479 (2015); English translation : Ukr. Math. J., 67, No. 4, 528–541 (2015).Google Scholar
- 5.E. A. Sevost’yanov, “On the equicontinuity of homeomorphisms with unbounded characteristic,” Mat. Trudy, 15, No. 1, 178–204 (2012).Google Scholar
- 9.K. Kuratowski, Topology, Vol. 2, Academic Press, New York (1968).Google Scholar