New topologies derived from the old one via operators
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 2X{2}^{X}, where 2X{2}^{X} is the power set of XX. We obtain some of their...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-04-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2024-0094 |
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| Summary: | 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 2X{2}^{X}, where 2X{2}^{X} is the power set of XX. 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. |
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| ISSN: | 2391-4661 |