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7 results on '"Goswami, Kabindra"'

1. Homotopical selection principles in bitopological dynamical systems

Author

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

Subjects
Mathematics - Dynamical Systems, Mathematics - General Topology, 54E55, 37B20, 37B99, 55P05, 55P1
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.

Published
2022

2. Erratum to ' Almost Menger property in bitopological spaces'

Author

Acharjee, Santanu and Goswami, Kabindra

Subjects
Mathematics - General Topology, 54E55
Abstract

In this paper, theorem 3.2 and theorem 4.1 of \"{O}z\c{c}a\u{g} and Eysen [S. \"{O}z\c{c}a\u{g} and A.E. Eysen, Almost Menger property in bitopological spaces, Ukrainian Math. J., {\bf 68}, No 6, 950-958 (2016)] are proven to be incorrect. An example is provided to disprove them and thus, correct versions of the theorems are restated.

Published
2022

3. Entropy of a Pairwise Continuous Map in NWPC Bitopological Dynamical Systems

Author

Acharjee, Santanu, Goswami, Kabindra, Sarmah, Hemanta Kumar, Gowda, G. D. Veerappa, Editor-in-Chief, Kesavan, S., Editor-in-Chief, Nekka, Fahima, Editor-in-Chief, Khan, Akhtar A., Editorial Board Member, Rangarajan, Govindan, Editorial Board Member, Balachandran, K., Editorial Board Member, Sreenivasan, K. R., Editorial Board Member, Brokate, Martin, Editorial Board Member, Nashed, M. Zuhair, Editorial Board Member, Gupta, N. K., Editorial Board Member, Zahra, Noore, Editorial Board Member, Manchanda, Pammy, Editorial Board Member, Lozi, René Pierre, Editorial Board Member, Aslan, Zafer, Editorial Board Member, and Acharjee, Santanu, editor

Published
2023
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7. ON FORWARD ITERATED HAUSDORFFNESS AND DEVELOPMENT OF EMBRYO FROM ZYGOTE IN BITOPOLOGICAL DYNAMICAL SYSTEMS.

Author

ACHARJEE, Santanu, GOSWAMI, Kabindra, and SARMAH, Hemanta Kumar

Subjects
*DYNAMICAL systems, *ZYGOTES, *HAUSDORFF spaces, *TOPOLOGICAL spaces, *EMBRYOS, *MITOSIS
Abstract

Topological dynamical system is an area of dynamical system to investigate dynamical properties in terms of a topological space. Nada and Zohny [Nada, S.I. and Zohny, H., An application of relative topology in biology, Chaos, Solitons and Fractals. 42 (2009), 202-204] applied topological dynamical system to explore the development process of an embryo from the zygote until birth and made three conjectures. In this paper, we disprove conjecture 3 of Nada and Zohny [Nada, S.I. and Zohny, H., An application of relative topology in biology, Chaos, Solitons and Fractals. 42 (2009), 202-204] by applying some of our mathematical results of bitopological dynamical system. Also, we introduce forward iterated Hausdorff space, backward iterated Hausdorff space, pairwise iterated Hausdorff space and establish relations between them in bitopological dynamical system. We formulate the function that represents cell division (specially, mitosis) and using this function we show that in the development process of a human baby from the zygote until its birth, there is a stage where the developing stage is forward iterated Hausdorff. [ABSTRACT FROM AUTHOR]

Published
2020
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