Dimension scales of bicompacta

We introduce the notion of a (stable) dimension scale $d-sc(X)$ of a space $X$, where $d$ is a dimension invariant. A bicompactum $X$ is called dimensionally unified if $\dim F=\dim_GF$ for every closed $F\subset X$ and for an arbitrary abelian group $G$. We prove that there exist dimensionally unified bicompacta with every given stable scale $\dim-sc$.