CANTER MANIFOLDS IN THE THEORY OF TRANSFINITE DIMENSION

For every countable non-limit ordinal alpha we construct an alpha-dimensional Canter ind-manifold, i.e., a compact metrizable space Z(alpha) such that ind Z(alpha) = alpha, and no closed subset L of Z(alpha) with ind L less than the predecessor of alpha is a partition in Z(alpha). An alpha-dimensional Canter Ind-manifold can be constructed similarly.