Erratum to "On $\beta $-Local Functions in Ideal Topological Spaces" and New Results

Abstract

In 2020, Powar et al. [P.L. Powar, T. Noiri and S. Bhadauria, \textit{ On $\beta $-local functions in ideal topological spaces}, European Journal of Pure and Applied Mathematics, \textbf{13}(4), (2020), 758-765] introduced $\beta$-local functions and studied related properties. The purpose of this paper is to show that Theorem $1(2)$, Theorem $2(4)$ and Theorem $3$ of Powar et al. [P.L. Powar, T. Noiri and S. Bhadauria, \textit{On $\beta$-local functions in ideal topological spaces}, European Journal of Pure and Applied Mathematics, \textbf{13}(4), (2020), 758-765] are not true. To disprove their claims, we provide a suitable example and justifications. Thus, we rectify their claims using our results and establish the correct results.

Keywords

• ideal topological space
• $\beta$-open set
• $\beta$-local function
• operation $cl_{\beta}^{*}$
• $\tau_{\beta}^{*}$-sets

Supporting Institution

Muğla Sıtkı Koçman University

Project Number

20/113/03/1

Thanks

This study has been supported by the Scientific Research Project Fund of Muğla Sıtkı Koçman University under the project number 20/113/03/1.

References

1. [1] K. Kuratowski, Topologie I, Warszawa, 1933.
2. [2] P.L. Powar, T. Noiri and S. Bhadauria, On b-local functions in ideal topological spaces, European Journal of Pure and Applied Mathematics, 13(4), (2020), 758-765.
3. [3] M.E. Abd El-Monsef, S.N. El-Deeb and R.A. Mahmoud, b-open sets and b-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77-90.