The ℜ_a operator in ideal topological spaces

Al-Omari, Wadei Faris, Noorani, Mohd Salmi Md., Noiri, T. and Al-Omeri, A.

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creative_2016_25_1_01_10

DOI: https://doi.org/10.37193/CMI.2016.01.01

Issue no: Vol 25/2016 no. 1 Tags: a-local function, a-open sets, $\Re_{a}$-operator, Ideal topological space

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Given a topological space $(X,\tau)$ an ideal $\mathcal{I}$ on $X$ and $A \subseteq X$ . The concept of $a$ -local function defined as follows $A^{a^\ast}(\mathcal{I},\tau)=\{x \in X: U \cap A \notin \mathcal{I}, \,\text{for every}\,\, U \in \tau^{a}(x)\}$ . In this paper a new type of space has been introduced with the help of $a$ -open sets and the ideal topological space called \textbf{ $a$ }-ideal space. Also we introduce an operator $\Re_a : \wp(X)\rightarrow \tau$ have been discussed, for every $A \in \wp(X)$ . We utilize the $\Re_a-$ operator to define interesting generalized $a$ -open sets and study their properties.