On homological dimension modulo $p$

The article provides a construction of an infinite-dimensional compact space of dimension 2 modulo $p$ for any $p$. A characterization of compact spaces $n$-dimensional modulo $p$ in terms of inverse spectrum of polyhedra is given. It is proved that compact spaces $n$-dimensional modulo $p$, and only these spaces, are images of $n$-dimensional compact spaces under maps acyclic in the sense of cohomology with coefficients in $\mathbf Z_p$.
Bibliography: 18 titles.