In this study, a $ \zeta^*_\Gamma $-local function is defined and its properties are examined. This newly defined local function is compared with the well-known local function and the local closure function according to the relation of being a subset. With the help of this new local function, the $ \Psi_{\zeta^*_\Gamma} $ operator is defined and topologies are obtained. Moreover, alternative answers are given to an open question found in the literature. $ \Psi_{\zeta^*_\Gamma} $-compatibility is defined and its properties are examined. $ \Psi_{\zeta^*_\Gamma} $-compatibility is characterized with the help of the new operator. Finally, new spaces were defined and characterized.
Citation: Ferit Yalaz, Aynur Keskin Kaymakcı. A new local function and a new compatibility type in ideal topological spaces[J]. AIMS Mathematics, 2023, 8(3): 7097-7114. doi: 10.3934/math.2023358
In this study, a $ \zeta^*_\Gamma $-local function is defined and its properties are examined. This newly defined local function is compared with the well-known local function and the local closure function according to the relation of being a subset. With the help of this new local function, the $ \Psi_{\zeta^*_\Gamma} $ operator is defined and topologies are obtained. Moreover, alternative answers are given to an open question found in the literature. $ \Psi_{\zeta^*_\Gamma} $-compatibility is defined and its properties are examined. $ \Psi_{\zeta^*_\Gamma} $-compatibility is characterized with the help of the new operator. Finally, new spaces were defined and characterized.
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Ferit Yalaz, Aynur Keskin Kaymakcı. A new local function and a new compatibility type in ideal topological spaces[J]. AIMS Mathematics, 2023, 8(3): 7097-7114. doi: 10.3934/math.2023358
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