Cantor manifolds in the theory of transfinite dimension
Volume 145 / 1994
Fundamenta Mathematicae 145 (1994), 39-64
DOI: 10.4064/fm-145-1-39-64
Abstract
For every countable non-limit ordinal α we construct an α-dimensional Cantor ind-manifold, i.e., a compact metrizable space $Z_α$ such that $ind Z_α = α$, and no closed subset L of $Z_α$ with ind L less than the predecessor of α is a partition in $Z_α$. An α-dimensional Cantor Ind-manifold can be constructed similarly.
