F-mixing and weak disjointness |
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Affiliation: | Department of Mathematics, University of Science and Technology of China, Hefei 230026, People''s Republic of China |
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Abstract: | A topological system (X,f) is -transitive if for each pair of opene subsets U and V of X, , where is a collection of subsets of which is hereditary upward. (X,f) is -mixing if (X×X,f×f) is -transitive. In this paper -mixing systems are characterized in terms of the chaoticity of the systems. Moreover, weak disjointness is studied via family. We will give conditions such that a dual theorem of the Weiss–Akin–Glasner theorem holds. Examples with this dual theorem fails for some “good” families are obtained. |
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