Cell-like mappings and nonmetrizable compacta of finite cohomological dimension

Abstract

Compact Hausdorff spaces X X of cohomological dimension dim Z X ≤ n {\dim _Z}X \leq n are characterized as cell-like images of compact Hausdorff spaces Z Z with covering dimension Z ≤ n Z \leq n . The proof essentially uses the newly developed techniques of approximate inverse systems.