Extension of mappings into CW-complexes

It is determined under what conditions the standard problem of extension of a mapping $f\colon A\to M$ to the whole space $X$ is solvable for any closed subset $A\subset X$. For finite-dimensional metric compacta $X$ and CW-complexes $M$ this is equivalent to the system of inequalities $\textrm{c-}{\dim}_{\pi_k(M)}X\leqslant k$. The result is applied to finding conditions for general position of a compactum in a Euclidean space.