On the Zero-Dimensionality of the Limit of the Sequence of Generalized Quasiconformal Mappings

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 $f\mspace{2mu}\colon D\to {\mathbb R}^n$ of a domain $D\subset{\mathbb R}^n$, $n\ge 2$, 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.