## Extreme Relations for Topological Flows

### Volume 53 / 2005

Bulletin Polish Acad. Sci. Math. 53 (2005), 17-24
MSC: Primary 37B05; Secondary 37B40, 37A35.
DOI: 10.4064/ba53-1-3

#### Abstract

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.