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- W4288364144 abstract "We consider a locally path-connected compact metric space $K$ with finite first Betti number $b_1(K)$ and a flow $(K, G)$ on $K$ such that $G$ is abelian and all $G$-invariant functions $finmathrm{C}(K)$ are constant. We prove that every equicontinuous factor of the flow $(K, G)$ is isomorphic to a flow on a compact abelian Lie group of dimension less than $b_1(K)$. For this purpose, we use and provide a new proof for [HJop, Theorem 2.12] which states that for a flow on a locally connected compact space the quotient map onto the maximal equicontinuous factor is monotone, i.e., has connected fibers. Our alternative proof is a simple consequence of a new characterization of the monotonicity of a quotient map $pcolon Kto L$ between locally connected compact spaces $K$ and $L$ that we obtain by characterizing the local connectedness of $K$ in terms of the Banach lattice $mathrm{C}(K)$." @default.
- W4288364144 created "2022-07-29" @default.
- W4288364144 creator A5082642184 @default.
- W4288364144 date "2019-04-27" @default.
- W4288364144 modified "2023-09-24" @default.
- W4288364144 title "On equicontinuous factors of flows on locally path-connected compact spaces" @default.
- W4288364144 doi "https://doi.org/10.48550/arxiv.1904.12203" @default.
- W4288364144 hasPublicationYear "2019" @default.
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