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September 2018 A note on the new set operator $\psi_{r}$
Arife Atay, Hasan İlhan Tutalar
Tbilisi Math. J. 11(4): 43-52 (September 2018). DOI: 10.32513/tbilisi/1546570884


Recently many published works made on local function used in ideal topological spaces can be found in related literature. "Semi Local Functions in Ideal Topological Spaces", "Closure Local Functions", and "$()^p$ and $\psi_p$-Operator" can be mentioned among such works those aim to define such functions. In general, the researchers prefer using the generalized open sets instead of topology in ideal topological spaces. Obtaining a Kuratowski closure operator with the help of local functions is an important detail in ideal topological space. However, it is not possible to obtain a Kuratowski closure operator from many of these local functions proposed by the above mentioned works. In order to address the lack of such an operator, the goal of this paper is to introduce another local function to give possibility of obtaining a Kuratowski closure operator. On the other hand, regular local functions defined for ideal topological spaces have not been found in the current literature. Regular local functions for the ideal topological spaces has been described within this work. Moreover, with the help of regular local functions Kuratowski closure operators $cl_I^{*r}$ and $\tau^{*r}$ topology are obtained. Many theorems in the literature have been revised according to the definition of regular local functions.


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Arife Atay. Hasan İlhan Tutalar. "A note on the new set operator $\psi_{r}$." Tbilisi Math. J. 11 (4) 43 - 52, September 2018.


Received: 20 November 2017; Accepted: 10 July 2018; Published: September 2018
First available in Project Euclid: 4 January 2019

zbMATH: 07172287
MathSciNet: MR3954206
Digital Object Identifier: 10.32513/tbilisi/1546570884

Primary: 54A05
Secondary: 54C10

Rights: Copyright © 2018 Tbilisi Centre for Mathematical Sciences


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Vol.11 • No. 4 • September 2018
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