Notions of \(\beta \)-closure compatible topology with an ideal. (English) Zbl 07898833
Summary: In this paper, we have defined \(\beta \)-local closure function. Its properties and characterizations are analyzed. The set operator is defined and its properties are discussed. The notions of \(\beta \)-closure compatible topology with an ideal \(\mathcal{J}\) are introduced and investigated. Moreover, -dense set and \(\beta_{\ast \ast} \)-codense ideal are defined and explored.
MSC:
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54F65 | Topological characterizations of particular spaces |
Keywords:
ideal; \( \beta \)-local closure function; \( \beta \)-open set; \( \beta_{\ast \ast} \)-codense idealReferences:
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