On conjecture 2 of Nada and Zohny from the perspective of bitopological dynamical systems

Abstract

Bitopological dynamical system is a recently explored area of dynamical system to investigate dynamical properties in terms of a bitopological space. Nada and Zohny [S.I. Nada, H. Zohny, An application of relative topology in biology, Chaos, Solitons and Fractals. 42 (2009), 202–204] explored the use of topological dynamical system in the development of an organism from zygote until birth and they made three conjectures regarding the development of child growth from zygote to till its birth. In this paper, we disprove the conjecture 2 of Nada and Zohny [S.I. Nada, H. Zohny, An application of relative topology in biology, Chaos, Solitons and Fractals. 42 (2009), 202–204] by applying some mathematical results from bitopological dynamical system, which was recently introduced by Acharjee et al. [S. Acharjee, K. Goswami, H.K. Sarmah, Transitive map in bitopological dynamical systems, (communicated)] with medical evidences. Also, we introduce forward iterated connected space, backward iterated connected space, pairwise iterated connected space and establish some of their relations with pairwise connectedness in bitopological dynamical system. We show that during the development of an organism from zygote until birth, the developing stage after gastrulation is pairwise disconnected and forward iterated disconnected.