Open AccessTransitive maps in bitopological dynamical systems
Author(s) -
Santanu Acharjee,
Kabindra Goswami,
Hemanta Sarmah Kumar
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2106011a
Subject(s) - transitive relation , mathematics , pairwise comparison , homeomorphism (graph theory) , iterated function , compact space , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , statistics
This paper introduces fundamental ideas of bitopological dynamical systems. Here, notions of bitopological transitivity, point transitivity, pairwise iterated compactness, weakly bitopological transitivity, etc. are introduced. Later, it is shown that under pairwise homeomorphism, weakly point transitivity implies weakly bitopological transitivity. Moreover, under pairwise homeomorphism; pairwise compactness and pairwise iterated compactness are found to be equivalent. Later, we apply our results in the development process of a human embryo from the zygote until birth. During the process of biological application, we disprove conjecture 1 of Nada and Zohny [S. I. Nada, H. Zohny, An application of relative topology in biology. Chaos, Solitons and Fractals, 42 (2009) 202-204].