Abstract
We introduce and study here the notion of distributional chaos on uniform spaces. We prove that if a uniformly continuous self-map of a uniform locally compact Hausdorff space has topological weak specification property then it admits a topologically distributionally scrambled set of type 3. This extends result due to Sklar and Smítal (J Math Anal Appl 241:181–188, 2000). We also justify through examples necessity of the conditions in the hypothesis of the main result.
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Shah, S., Das, T. & Das, R. Distributional Chaos on Uniform Spaces. Qual. Theory Dyn. Syst. 19, 4 (2020). https://doi.org/10.1007/s12346-020-00344-x
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DOI: https://doi.org/10.1007/s12346-020-00344-x