Research Article
Types of Generalized Open Sets with Ideal
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 80 - Issue 4 |
| Published: October 2013 |
| Authors: Rodyna A. Hosny, Deena Al-Kadi |
10.5120/13848-1681
|
Rodyna A. Hosny, Deena Al-Kadi . Types of Generalized Open Sets with Ideal. International Journal of Computer Applications. 80, 4 (October 2013), 11-14. DOI=10.5120/13848-1681
@article{ 10.5120/13848-1681,
author = { Rodyna A. Hosny,Deena Al-Kadi },
title = { Types of Generalized Open Sets with Ideal },
journal = { International Journal of Computer Applications },
year = { 2013 },
volume = { 80 },
number = { 4 },
pages = { 11-14 },
doi = { 10.5120/13848-1681 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2013
%A Rodyna A. Hosny
%A Deena Al-Kadi
%T Types of Generalized Open Sets with Ideal%T
%J International Journal of Computer Applications
%V 80
%N 4
%P 11-14
%R 10.5120/13848-1681
%I Foundation of Computer Science (FCS), NY, USA
Abstract
The aim of this paper is to introduce and study the notions of ? (resp. , pre, semi, ?)-open sets in terms of an ideal I. These concepts generalize the usual notions of ? (resp. , pre, semi, ?) open sets. Also, several of their topological properties are investigated.
References
- Abd El-Monsef, M. . E. , El-Deeb, S. N. , and Mahmould, R. A. 1983. ?-open sets and ?-continuous mapping. Bull. Fac. Sci. Assiut Univ. , 12, 77-90.
- Andrijevic, D. 1986. Semi-preopen sets, Mat. Vesnik, 38, 24 – 32.
- Hamlett, T. R. , and Jankovic, D. 1992. Compatible extensions of ideals, Boll. Un. Mat. Ita. , 7, 453 - 465.
- Jafari, S. , and Rajesh, N. 2011. Generalized closed sets with respect to ideals, Eur. J. Pure Appl. Math, 4(2), 147 - 151.
- Jankovic, D. , and Hamlett, T. R. 1990. New topologies from old via ideals, Amer. Math. Month. , 97, 295 - 310.
- Jankovic, D. , and Reilly, I. 1985. On semi-separation properties, Indian J. Pure Appl. Math. 16, 957 - 964.
- Julian Dontchev, 1998. Survey on pre-open sets. The Proceedings of the Yatsushiro topological conference, 1-18.
- Kelley, J. L. , 1955. General Topology, D. Van Nastrand Company, Inc.
- Levine, N. , 1963. Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly 70, 36 - 41.
- Mashhour, A. S. , Abd El-Monsef, M. E. , and El-Deeb, S. N. , 1982. On pre-continuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53, 47 - 53.
- Mashhour, A. S. , Abd El-Monsef, M. E. , and Hasanein, I. A. , 1984. On pretopological spaces, Bull. Math. R. S. Roumanie (N. S) 28(76), 39 - 45.
- Michael, F. , 2013. On semi-open sets with respect to an ideal, Eur. J. Pure Appl. Math, 6, 53 - 58.
- Njastad, O. , 1965. On some classes of nearly open sets, Pacific J. Math 15, 961 –970.
- Rodyna A. Hosny, 2013. Pre-open sets with ideal, European Journal of Scientific Research, 104 (1), 99 -101.
Index Terms
Keywords