IJPAM: Volume 118, No. 3 (2018)

Title

OPERATION ON SEMI GENERALIZED OPEN SETS
WITH ITS SEPARATION AXIOMS

Authors

Baravan A. Asaad$^{1,2}$, Nazihah Ahmad$^3$
$^1$Department of Computer Science
College of Science
Cihan University-Duhok, Kurdistan-region, IRAQ
$^2$Department of Mathematics
Faculty of Science
University of Zakho
Kurdistan-region, IRAQ
$^3$School of Quantitative Sciences
College of Arts and Sciences
Universiti Utara Malaysia
06010 Sintok, Kedah, MALAYSIA

Abstract

The aim of this paper is to introduce the concept of an operation $\gamma$ on the class of all semi-generalized open sets in topological spaces. Using this operation, we define a new concept called semi-generalized-$\gamma$-open ($sg$-$\gamma$-open) sets and study some of their related properties. We found that the relation between this new concept and $sg$-open set are independent. In addition, we study some separation axioms called $sg$-$\gamma$-$T_i$ for $i = 0, 1, 2$. Some basic properties and relations of these separation axioms are obtained.

History

Received: 2017-12-11
Revised: 2018-02-22
Published: April 15, 2018

AMS Classification, Key Words

AMS Subject Classification: 54A05, 54A10, 54D10
Key Words and Phrases: Operation $\gamma$ on $\tau_{sg}$, $sg$-$\gamma$-open sets, $sg$-$\gamma$-$T_i$ spaces ( $i \in \{0,1, 2\}$)

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
T.V. An, D.X. Cuong and H. Maki, On operation-preopen sets in topological spaces, Scientiae Mathematicae Japonicae Online, 68 1 (2008), 11-30, (e-2008), 241-260.

2
B.A. Asaad, Some Applications of Generalized Open Sets via Operations, New Trends in Mathematical Sciences, 5 1 (2017), 145-157.

3
P. Bhattacharyya and B.K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29 3 (1987), 375-382.

4
C. Carpintero, N. Rajesh and E. Rosas, Operation approaches on $b$-open sets and applications, Bulletin of Parana's Mathematical Society, 30 1 (2012), 21-33.

5
S.G. Crossley and S.K. Hildebrand, Semi-closure, Texas Journal of Science, 22 (1971), 99-112.

6
D. S. Jankovic, On functions with $\alpha$-closed graphs, Glasnik Matematicki, 18 38 (1983), 141-148.

7
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 1 (1963), 36-41.

8
S. Kasahara, Operation compact spaces, Math. Japonica, 24 1 (1979), 97-105.

9
G. S. S. Krishnan, M. Ganster and K. Balachandran, Operation approaches on semi-open sets and applications, Kochi Journal of Mathematics, 2 (2007), 21-33.

10
H. Ogata, Operation on topological spaces and associated topology, Math. Japonica, 36 1 (1991), 175-184.

11
S. Tahiliani, Operation approach to $\beta$-open sets and applications, Mathematical Communications, 16 (2011), 577-591.

How to Cite?

DOI: 10.12732/ijpam.v118i3.17 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 118
Issue: 3
Pages: 701 - 711


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).