Snake-like bicompacta and some problems of dimensional theory (Q1082639)

The author proves the existence, for every \(n\geq 1\), of a completely normal snake-like bicompactum \(X_ n\) such that ind \(X_ n=n\). In addition, a negative answer is given to the question posed by Engelking and Pol whether there exists a one-dimensional (in the sense of dim) hereditarily normal bicompactum that cannot be represented as a sum of a countable number of zero-dimensional subspaces.