On the zero-dimensionality of the limit of the sequence of generalized quasiconformal mappings

Abstract

The paper is devoted to the study of the properties of a class of space mappings that is more general than that of bounded distortion mappings (aka quasiregular mappings). It is shown that the locally uniform limit of a sequence of mappings f: D → ℝⁿ of a domain D ⊂ ℝⁿ, n ≥ 2, satisfying one inequality for the p-modulus of families of curves is zero-dimensional. This statement generalizes a well-known theorem on the openness and discreteness of the uniform limit of a sequence of bounded distortion mappings.