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Localic transitivity

Abstract

For a dynamical system (Xf), the notion of topological transitivity has been studied by some researchers. There are several definitions of this property, and it is part of the folklore of dynamical systems that under some hypotheses, they are equivalent. In this paper, our aim is to introduce and study some properties of topological transitivity in pointfree topology, for which we first need to define in a way what makes them conservative extensions of topological transitivity defined by G.D. Birkhoff. We describe the way the different properties are related to each other in pointfree topology.

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Acknowledgements

Thanks are due to the referee for helpful comments that have improved the readability of this paper and for providing Proposition 3.2.

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Correspondence to Ali Akbar Estaji.

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Communicated by Presented by A. Dow.

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Estaji, A.A., Robat Sarpoushi, M. & Barzanouni, A. Localic transitivity. Algebra Univers. 83, 29 (2022). https://doi.org/10.1007/s00012-022-00783-4

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  • DOI: https://doi.org/10.1007/s00012-022-00783-4

Keywords

  • Topologically transitive
  • Transitive point
  • Sublocale
  • Localic map

Mathematics Subject Classification

  • 06D22
  • 54C05
  • 37B99