In this paper we investigate a question of Akin and Carlson regarding the existence of transitive dynamical systems on a separable compact Hausdorff space without dense orbits. In particular, we give an answer in ZFC for the class of perfectly normal spaces and a consistent solution in the realm of hereditarily normal spaces.
On a problem of Akin and Carlson on dense orbits and transitivity / LE DONNE, Attilio; Le Donne, Alessandro; Fedeli, Alessandro. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - 239:(2018), pp. 244-250. [10.1016/j.topol.2018.03.001]
On a problem of Akin and Carlson on dense orbits and transitivity
Attilio Le Donne;
2018
Abstract
In this paper we investigate a question of Akin and Carlson regarding the existence of transitive dynamical systems on a separable compact Hausdorff space without dense orbits. In particular, we give an answer in ZFC for the class of perfectly normal spaces and a consistent solution in the realm of hereditarily normal spaces.File allegati a questo prodotto
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