Stefan GeschkeThe nonexistence of universal metric flows

Comment.Math.Univ.Carolin. 59,4 (2018) 487-493.

Abstract:We consider dynamical systems of the form $(X,f)$ where $X$ is a compact metric space and $f\colon X\to X$ is either a continuous map or a homeomorphism and provide a new proof that there is no universal metric dynamical system of this kind. The same is true for metric minimal dynamical systems and for metric abstract $\omega$-limit sets, answering a question by Will Brian.

Keywords: universal metric dynamical system; minimal dynamical system

DOI: DOI 10.14712/1213-7243.2015.264
AMS Subject Classification: 54H20 37B05 37B10

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