October 13, 2025Open Access

On Dynamical System and Topological Transitivity via Ideals

Key Points

Topological transitivity is redefined through equivalent conditions, enhancing the understanding of dynamical systems.
The paper highlights equivalence between $ extbf{I}$-denseness, $*$-denseness, and denseness under complete codensity.
The approach utilizes an amendment to a previous result, emphasizing the importance of ideal conditions.
These findings potentially reshape mathematical frameworks in studying dynamical systems through ideal theory.

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 LL2013. Corrected version of the Remark: ``If I is codense, then I-denseness, *-denseness and denseness are equivalent" will be ``If I is completely codense, then I-denseness, *-denseness and denseness are equivalent".

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Cite This Study

Mıah et al. (Mon,) studied this question.

synapsesocial.com/papers/68ece2abd1bb2827d12971e7 https://doi.org/https://doi.org/10.48550/arxiv.2503.01241