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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-3-6,
author = {Pierre-Paul Romagnoli},
title = {A remark on the topological entropies of covers and partitions},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {273-281},
zbl = {1123.37009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-3-6}
}
Pierre-Paul Romagnoli. A remark on the topological entropies of covers and partitions. Studia Mathematica, Tome 178 (2007) pp. 273-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-3-6/