@article{Qahis2026, 
author = {Abdo Qahis and Mohd Salmi Md Noorani},
title = {The        ω          ♯      -operator in ideal topological spaces and its associated topology},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {17039-17061},
keywords = {ideal topological space, ω-open set, (⋅)ω♯-operator, Clω♯- operator, Tω♯-topology, Tω∗-topology, ω∗-continuity, ω♯-continuity},
url = {https://www.sciopen.com/article/10.3934/math.2026698},
doi = {10.3934/math.2026698},
abstract = {In this paper, we introduced a new set-theoretic operator    (  ⋅      )          ω              ♯       in the framework of ideal topological spaces and investigated its fundamental properties, including its connections with the classical    ♯-operator and the    ω-local function. Using this operator, we defined a closure-type operator              C      l              ω              ♯       and showed that it satisfies the Kuratowski closure axioms. Consequently, a topology              T              ω              ♯       was obtained, which is strictly finer than the topology induced by the    ♯-operator. Furthermore, the structural relationships among these topologies were examined, and some applications of the        ω    ♯  -operator were presented. Finally, we introduced the notions of        ω    ∗  -continuity and        ω    ♯  -continuity, investigated their relationship, and established a new decomposition of continuity. We also compared these notions with related concepts such as    ω-continuity and    ♯-continuity.}
}