Transitivities of maps of general topological spaces |
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Authors: | Jie-Hua Mai |
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Institution: | a Institute of Mathematics, Shantou University, Shantou, Guangdong, 515063, PR China b Department of Mathematics, Shandong University at Weihai, Weihai, Shandong, 264209, PR China |
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Abstract: | In this paper we investigate orbit-transitivity, strong orbit-transitivity, ω-transitivity and open-set-transitivity of maps of general topological spaces. The relation between these transitivities is studied. We discuss various topological spaces, containing pseudo-regular spaces, partially completable spaces, and topological spaces without quasi-isolated points. Several conditions on spaces and on continuity for one transitivity to imply another transitivity are given. |
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Keywords: | primary 54H20 secondary 37B20 37D45 |
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