• Title/Summary/Keyword: strongly ${\mu}^{\circ}$-codense

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ON 𝜃-MODIFICATIONS OF GENERALIZED TOPOLOGIES VIA HEREDITARY CLASSES

  • Al-Omari, Ahmad;Modak, Shyamapada;Noiri, Takashi
    • Communications of the Korean Mathematical Society
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    • v.31 no.4
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    • pp.857-868
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    • 2016
  • Let (X, ${\mu}$) be a generalized topological space (GTS) and $\mathcal{H}$ be a hereditary class on X due to $Cs{\acute{a}}sz{\acute{a}}r$ [8]. In this paper, we define an operator $()^{\circ}:\mathcal{P}(X){\rightarrow}\mathcal{P}(X)$. By setting $c^{\circ}(A)=A{\cup}A^{\circ}$ for every subset A of X, we define the family ${\mu}^{\circ}=\{M{\subseteq}X:X-M=c^{\circ}(X-M)\}$ and show that ${\mu}^{\circ}$ is a GT on X such that ${\mu}({\theta}){\subseteq}{\mu}^{\circ}{\subseteq}{\mu}^*$, where ${\mu}^*$ is a GT in [8]. Moreover, we define and investigate ${\mu}^{\circ}$-codense and strongly ${\mu}^{\circ}$-codense hereditary classes.