Showing 1–1 of 1 results for author: Baimani, N

Transitivities of maps of generalized topological spaces

Authors: M. R. Ahmadi Zand, N. Baimani

Abstract: In this work, we present several new findings regarding the concepts of orbit-transitivity, strict orbit-transitivity, $ω$-transitivity, and $μ$-open-set transitivity for self-maps on generalized topological spaces. Let $(X,μ)$ denote a generalized topological space. A point $x \in X$ is said to be \textit{quasi-$μ$-isolated} if there exists a $μ$-open set $U$ such that $x \in U$ and… ▽ More In this work, we present several new findings regarding the concepts of orbit-transitivity, strict orbit-transitivity, $ω$-transitivity, and $μ$-open-set transitivity for self-maps on generalized topological spaces. Let $(X,μ)$ denote a generalized topological space. A point $x \in X$ is said to be \textit{quasi-$μ$-isolated} if there exists a $μ$-open set $U$ such that $x \in U$ and $i_μ(U \setminus c_μ(\{x\})) = \emptyset$. We prove that $x$ is a quasi-$μ$-isolated point of $X$ precisely when there exists a $μ$-dense subset $D$ of $X$ for which $x$ is a $μ_D$-isolated point of $D$. Moreover, in the case where $X$ has no quasi-$μ$-isolated points, we establish that a map $f: X \to X$ is orbit-transitive (or strictly orbit-transitive) if and only if it is $ω$-transitive. △ Less

Submitted 9 November, 2025; originally announced November 2025.

Comments: 9 pages

MSC Class: 54A05; 37C35