Devaney's and Li-Yorke's chaos in uniform spaces
Let \(X\) be a second countable Baire Hausdorff uniform space without isolated points. The following is the main result in this paper. Theorem. Let \(G\) be an Abelian group on \(X\). If a continuous action of \(G\) on \(X\) is chaotic in the Devaney sense, then there exists an uncountable dense scrambled set; so that, it is chaotic in the Li-Yorke sense. Further aspects occasioned by these developments are also discussed.
scientific article; zbMATH DE number 6845714