On the Convergence of Mappings in Metric Spaces with Direct and Inverse Modulus Conditions
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For mappings in metric spaces satisfying one inequality for the modulus of families of curves, we establish the property of lightness of the limit mapping. It is shown that the uniform limit of these mappings is a light mapping, whenever the majorant responsible for the distortion of the families of curves is of finite mean oscillation at any point. In addition, for one class of homeomorphisms of metric spaces, we prove theorems on the equicontinuity of the families of inverse mappings.
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