New topologies derived from the old one via operators
Year: 2025
Type: article
Abstract: The main purpose of this work is to study the ideal topology defined by the minimal and maximal ideals on a topological space. Also, we define and investigate the concepts of ideal quotient and annihilator of any subfamily of 2 X {2}^{X} , where 2 X {2}^{X} is the power set of X X . We obtain some of their fundamental properties. In addition, several relationships among the above notions have been discussed. Moreover, we define a new topology on an ideal topological space, called sharp topology, via the sharp operator defined in this study, which turns out to be finer than the original topology. Furthermore, a decomposition of open sets (in the original topology) has been obtained. Finally, we conclude our work with some interesting applications.
Source: Demonstratio Mathematica
Authors: Faical Yacine Issaka, Murad Özkoç
Institution: Muğla University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4409283269