Correction to: Devaney’s and LiYorke’s Chaos in Uniform Spaces
 34 Downloads
Correction to: J Dyn Control Syst
https://doi.org/10.1007/s1088301793600
The original version of this article unfortunately contained a mistake.
And the set AR of the forth paragraph of Definition 2.4 should be denoted byElements x and y of X to be asymptotic if for any \(U \in \mathcal {U}\) and any \(\{G_{i} i \in \mathbb {N}\}\in \mathcal {G}\), there exists \(k \in \mathbb {N}\) such that (gx,gy) ∈ U for each \(g\in \bigcup _{i\in \mathbb {N}} G_{i} \backslash G_{k} \).

The phrase “let G be an Abelian group” in the statement of Theorem 1.2 is replaced by “let G be a countable Abelian group”. Similarly, the phrases “an Abelian group G” in Lemma 3.6 and Proposition 3.7 are replaced by “a countable Abelian group G”.

In the proof of Lemma 3.6, the phrase “Let \((G_{i})_{i\in \mathbb {N}}\) be an elements of \(\mathcal {G}\) with G_{1} = ∅” of the line 1 in the second paragraph should be replaced by “Let \((G_{i})_{i\in \mathbb {N}}\) be an elements of \(\mathcal {G}\) with G_{1} = ∅ and \(G=\bigcup _{i\in \mathbb {N}} G_{i} \)”.
The author is very grateful to Fatemah Ayatollah Zadeh Shirazi for pointing out the mistake and providing useful suggestions.
Notes
References
 1.Arai T. Devaney’s and LiYorke’s chaos in uniform spaces. J Dyn Control Syst 2018;24(1):93–100.MathSciNetCrossRefzbMATHGoogle Scholar