e*−Transitivity as an Extension to Chaos Notions

The introduction of e * -transitivity is motivated by the broader concept of e * -open sets, representing a generalised extension of various open set concepts.In this paper, we prove that the e * -transitivity implies the classical transitivity and many other types of transitivity such as b-transitivity, -transitivity, -transitivity, and sr-transitivity.Therefore, exploring the properties of e * -transitivity holds significance, as these properties extend to other forms of transitivity.Additionally, we introduce several e * -chaos notions that serve as analogoues, to their classical counterparts.These notions include total e * -transitivity, e * -mixing, e * -locally everywhere onto (abbreviated as e * -l.e.o.), and weak e * -blending.Subsequently, we demonstrate the interrelations among these newly introduced e * -chaos notions and illustrate their connections to classical chaos concepts.This comparative analysis not only enriches our understanding of e * -transitivity but also introduce new notions of chaos based on e * -transitivity.