Abstract

The purpose of this paper is to introduce various levels of connectedness in approximation spaces using some classes of near open sets. Moreover, proved results, examples and counter examples are provided.

Keywords

References

[1] M. E. Abd El-Monsef, S. N. El-Deeb, R. A. Mahmoud, -open sets and -continuous mappings, Bull. Fac. Sc. Assuit Univ., 12 (1983) 77-90.
[2] M. E. Abd El-Monsef, A. M. Kozae, M. J. Iqelan, On near open sets and near approximations, Jour. of Inst. of Mathematics & Computer Sciences (Computer Science Ser.), 20 (1) (2009) 99-109.
[3] M. E. Abd El-Monsef, A. M. Kozae, M. J. Iqelan, Near rough and near exact sets in topological spaces, Indian Journal of Mathematics and Mathematical Sciences, 5 (1) (2009) 49-58.
[4] M. E. Abd El-Monsef, A. M. Kozae, M. J. Iqelan, Near approximations in topological spaces, Int. Journal of Math. Analysis, 4 (6) (2010) 279-290.
[5] D. Andrijević, Semi-preopen sets, Ibid, 38 (1986) 24-32.
[6] D. Andrijević, On b-open sets, Mat. Vesnik, 48 (1996) 59-64.
[7] A. A. El-Atik, A study of some types of mappings on topological spaces, M.Sc. Thesis, Tanta Univ., Egypt, 1997.
[8] M. J. Iqelan, On topological structures and uncertainty, Ph.D. Thesis, Tanta Univ., Egypt, 2010.
[9] M. J. Iqelan, Rough Connected Topologized Approximation Spaces, Int. Journal of Math. Analysis, 8 (53) (2014) 2619-2628.
[10] M. J. Iqelan, Semi-rough Connected Topologized Approximation Spaces, Journal of Advances in Mathematics 9 (7) (2014) 2840-2846.
[11] M. J. Iqelan, Pre-rough Connected Topologized Approximation Spaces, International Journal of Mathematics Trends and Technology 16 (1) (2014) 39-45.
[12] J. Kelley, General topology, Van Nostrand Company, 1955.
[13] E. Lashin, A. Kozae, A. Abo Khadra and T. Medhat, Rough set theory for topological spaces, International Journal of Approximate Reasoning, 40 (2005) 35-43.
[14] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer Math. Monthly, 70 (1963), 36-41.
[15] T.Y. Lin, Topological and fuzzy rough sets, in: R. Slowinski (Ed.), Decision Support by Experience—Application of the Rough Sets Theory, Kluwer Academic Publishers, 1992, pp. 287–304.
[16] A. S. Mashhour, M. E. Abd El-Monsef, S. N. El-Deeb, On pre-continuous and weak pre-continuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982) 47-53.
[17] O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15 (1965) 961-970.
[18] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991.