Homotopical selection principles in bitopological dynamical systems

TL;DR

This paper introduces homotopical selection principles in bitopological dynamical systems, defining new homotopy concepts and properties, and explores their interrelations within this mathematical framework.

Contribution

It presents novel homotopical selection principles and related concepts specifically tailored for bitopological dynamical systems, expanding the theoretical understanding of their structure.

Findings

Defined BTDS-homotopy, iteration homotopy, and path homotopy.

Introduced H-Rothberger, H-Menger, PH-Rothberger, and PH-Menger properties.

Established connections among these properties in bitopological dynamical systems.

Abstract

Homotopy deals with the intuitive idea of continuous deformation of a continuous map between two topological spaces. In this paper, we introduce homotopical selection principles in bitopological dynamical systems. Here, we define $BTDS-$homotopy, $BTDS-$iteration homotopy and $BTDS-$path homotopy, and then using these notions we define various selection properties viz. H-Rothberger property, H-Menger property, PH-Rothberger property, PH-Menger property and their weaker versions. We also discuss several results connecting these concepts in bitopological dynamical systems.