A remark on the topological entropies of covers and partitions
Volume 182 / 2007
Studia Mathematica 182 (2007), 273-281
MSC: Primary 37B40; Secondary 37B10, 37A35.
DOI: 10.4064/sm182-3-6
Abstract
We study if the combinatorial entropy of a finite cover can be computed using finite partitions finer than the cover. This relates to an unsolved question in [R] for open covers. We explicitly compute the topological entropy of a fixed clopen cover showing that it is smaller than the infimum of the topological entropy of all finer clopen partitions.
