The continuously removable sets for quasiconformal mappings

Let $D$ be a domain in the $n$-dimensional Euclidean space $R^n$, $n\geqslant 2$, and let $E$ be a compact in $D$. The paper presents conditions on the compact $E$ under which any homeomorphic mapping $f\colon D\setminus E\rightarrow R^n$ can be extended to a continuous mapping $f\colon D\rightarrow\bar{R}^n=R^n\cup\{\infty\}$. These conditions define the class of NCS-compacts, which, for $n=2$, coincides with the class of topologically removable compacts for conformal and quasiconformal mappings.