We introduce the concept of an extreme relation for a topological flow as an analogue of the extreme measurable partition for a measure-preserving transformation considered by Rokhlin and Sinai, and we show that every topological flow has such a relation for any invariant measure. From this result, it follows, among other things, that any deterministic flow has zero topological entropy and any flow which is a K-system with respect to an invariant measure with full support is a topological K-flow.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-3,
author = {Brunon Kami\'nski and Artur Siemaszko and Jerzy Szyma\'nski},
title = {Extreme Relations for Topological Flows},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {17-24},
zbl = {1105.37007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-3}
}
Brunon Kamiński; Artur Siemaszko; Jerzy Szymański. Extreme Relations for Topological Flows. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 17-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-3/