Transitivities of maps of generalized topological spaces

2025/11/09 by Zand, M. R. Ahmadi, Baimani, N.
#37C35 #54A05 #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2511.06241

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 ∈ X is said to be quasi-μ-isolated if there exists a μ-open set U such that x ∈ U and i_μ(U ∖ c_μ(\x\)) = ∅. 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 → X is orbit-transitive (or strictly orbit-transitive) if and only if it is ω-transitive.

Citations

• On generalized topological groups

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