Extension of mappings of Bing spaces into ANRs

An atom is a hereditarily indecomposable continuum. A Bing space is a compactum in which every subcontinuum is an atom. E ⊂ K is a sample for K if E meets every component of K. σ(K) ⩽ n if K has a σ-compact sample E with dim E ⩽ n. Hence, if K has countably many components then σ(K) = 0. proved that if K is a closed subset of a Bing space X then 1. σ(K) = 0 then every map of K in a connected ANR extends upon X; f σ(K) ⩽ n then every map of K in Sn + 1 extends upon X. or extension of maps in Bing spaces σ(K) may replace dim K (since both (i) and (ii) hold for every space X, not just Bing spaces, if dim K ⩽ n).