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<p>Bitopological dynamical systems is a new area of dynamical systems recently introduced by Acharjee et al. in 2021. Homotopy, on the other hand, concerns the intuitive notion of deforming one continuous map into another between two topological spaces. Therefore, it is evident that homotopy offers wide applicability in bitopological dynamical systems. Yet, no prior work has explored the connection between homotopy and bitopological dynamical systems. In this paper, we propose homotopical selection principles in bitopological dynamical systems (<i>BTDS</i>). Specifically, we introduce the notions of <i>BTDS</i>–homotopy, <i>BTDS</i>–iteration homotopy, and <i>BTDS</i>–path homotopy. Building on these notions, we define various selection properties such as the H-Rothberger property, H-Menger property, PH-Rothberger property, PH-Menger property, along with their weaker variants. Furthermore, we establish and discuss several results linking these concepts within the framework of bitopological dynamical systems.</p>

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Homotopical selection principles in bitopological dynamical systems

  • 期刊论文

  • 发表日期：

    2025年11月10日

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  • Santanu Acharjee,
  • Kabindra Goswami,
  • Hemanta Kumar Sarmah

摘要

Bitopological dynamical systems is a new area of dynamical systems recently introduced by Acharjee et al. in 2021. Homotopy, on the other hand, concerns the intuitive notion of deforming one continuous map into another between two topological spaces. Therefore, it is evident that homotopy offers wide applicability in bitopological dynamical systems. Yet, no prior work has explored the connection between homotopy and bitopological dynamical systems. In this paper, we propose homotopical selection principles in bitopological dynamical systems (BTDS). Specifically, we introduce the notions of BTDS–homotopy, BTDS–iteration homotopy, and BTDS–path homotopy. Building on these notions, we define various selection properties such as the H-Rothberger property, H-Menger property, PH-Rothberger property, PH-Menger property, along with their weaker variants. Furthermore, we establish and discuss several results linking these concepts within the framework of bitopological dynamical systems.