Geodesic
Extension of mappings into CW-complexes
Sbornik. Mathematics, Tome 74 (1993) no. 1, pp. 47-56

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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. 
@article{SM_1993_74_1_a3,
     author = {A. N. Dranishnikov},
     title = {Extension of mappings into {CW-complexes}},
     journal = {Sbornik. Mathematics},
     pages = {47--56},
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     volume = {74},
     number = {1},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_74_1_a3/}
}
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A. N. Dranishnikov. Extension of mappings into CW-complexes. Sbornik. Mathematics, Tome 74 (1993) no. 1, pp. 47-56. http://geodesic.mathdoc.fr/item/SM_1993_74_1_a3/