On Dynamical System and Topological Transitivity via Ideals

Chhapikul Miah; Shyamapada Modak

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arXiv · 2503.01241

On Dynamical System and Topological Transitivity via Ideals

Chhapikul Miah·Shyamapada Modak

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Abstract

This paper will discuss the problem of defining the new topological transitivity. To do this several equivalent topological transitive and non-wandering point has been discussed through this paper. This paper also consider the ideal version of transitivity with the help of the amendment of the result Remark $6.9(2)$ of \cite{LL2013}. Corrected version of the Remark: ``If $\mathcal{\bf I}$ is codense, then $\mathcal{\bf I}$-denseness, $*$-denseness and denseness are equivalent" will be ``If $\mathcal{\bf I}$ is completely codense, then $\mathcal{\bf I}$-denseness, $*$-denseness and denseness are equivalent".

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BibTeX RIS

Chhapikul Miah, Shyamapada Modak. 2025-03-03. On Dynamical System and Topological Transitivity via Ideals. https://arxiv.org/abs/2503.01241

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