Hurewicz theorem for extension dimension

Abstract

We prove a new selection theorem for multivalued mappings of C-space. Using this theorem we prove extension dimensional version of Hurewicz theorem for a closed mapping f :X→Y of k-space X onto paracompact C-space Y: if for finite CW-complex M we have e-dim Y⩽[ M] and for every point y∈ Y and every compactum Z with e-dim Z⩽[ M] we have e-dim( f −1( y)× Z)⩽[ L] for some CW-complex L, then e-dim X⩽[ L].