The main goal of this paper is to construct, for every n,m ∈ ℕ, a hereditarily indecomposable continuum $X_{nm}$ of dimension m which has exactly n autohomeomorphisms.

The paper is devoted to generalizations of the Cencelj-Dranishnikov theorems relating extension properties of nilpotent CW complexes to their homology groups. Here are the main results of the paper: Theorem 0.1. Let L be a nilpotent CW complex and F the homotopy fiber of the inclusion i of L into its infinite symmetric product SP(L). If X is a metrizable space such that $X\tau K(H_k\left(L\right),k)$ for all k ≥ 1, then $X\tau K({\pi }_k\left(F\right),k)$ and $X\tau K({\pi }_k\left(L\right),k)$ for all k ≥ $.$Theorem 0.2. Let X be a metrizable space such that dim(X) < ∞ or X ∈ ANR. Suppose...

Let X be a compact metric space and let C(X) denote the space of subcontinua of X with the Hausdorff metric. It is proved that every two-dimensional continuum X contains, for every n ≥ 1, a one-dimensional subcontinuum $T_n$ with $dimC\left(T_n\right)\ge n$. This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.