Homological dimension and homogeneous ANR spaces

The homological dimension dG of metric compacta was introduced by Alexandroff in [1]. In this paper we provide some general properties of dG, mainly with an eye towards describing the dimensional full-valuedness of compact metric spaces. As a corollary of the established properties of dG, we prove that any two-dimensional lc2 metric compactum is dimensionally full-valued. This improves the well known result of Kodama [10] that every two-dimensional ANR is dimensionally full-valued. Applications for homogeneous metric ANR-compacta are also given.