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

Santanu Acharjee, Kabindra Goswami, Hemanta Kumar Sarmah

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.

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Published: 2020-12-04

How to Cite this Article:

Santanu Acharjee, Kabindra Goswami, Hemanta Kumar Sarmah, On conjecture 2 of Nada and Zohny from the perspective of bitopological dynamical systems, J. Math. Comput. Sci., 11 (2021), 278-291

Copyright © 2021 Santanu Acharjee, Kabindra Goswami, Hemanta Kumar Sarmah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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