## Tbilisi Mathematical Journal

- Tbilisi Math. J.
- Volume 11, Issue 4 (2018), 43-52.

### A note on the new set operator $\psi_{r}$

Arife Atay and Hasan İlhan Tutalar

#### Abstract

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.

#### Article information

**Source**

Tbilisi Math. J., Volume 11, Issue 4 (2018), 43-52.

**Dates**

Received: 20 November 2017

Accepted: 10 July 2018

First available in Project Euclid: 4 January 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.tbilisi/1546570884

**Digital Object Identifier**

doi:10.32513/tbilisi/1546570884

**Mathematical Reviews number (MathSciNet)**

MR3954206

**Subjects**

Primary: 54A05: Topological spaces and generalizations (closure spaces, etc.)

Secondary: 54C10: Special maps on topological spaces (open, closed, perfect, etc.)

**Keywords**

regular open set regular closed set ideal topological space local function regular local function

#### Citation

Atay, Arife; İlhan Tutalar, Hasan. A note on the new set operator $\psi_{r}$. Tbilisi Math. J. 11 (2018), no. 4, 43--52. doi:10.32513/tbilisi/1546570884. https://projecteuclid.org/euclid.tbilisi/1546570884