On supra R-open sets and some applications on topological spaces

M. E. El-Shafei; M. Abo-elhamayel; Tareq Al-shami

M. E. El-Shafei Department of Mathematics, Faculty of science, Mansoura University, Egypt
M. Abo-elhamayel Department of Mathematics, Faculty of science, Mansoura University, Egypt
Tareq Al-shami Department of Mathematics, Faculty of science, Sana’a University, Yemen

Keywords: Supra R-open set, Supra R-continuous (open, closed, homeomorphism) maps, SR-Ti-spaces (i=1, 2) and supra topological spaces.

Abstract

In the present paper a new class of generalized supra open sets called supra R-open set is introduced. The relationships between some generalized supra open sets and this class are investigated and illustrated with enough examples. Also, new types of supra continuous maps, supra open maps, supra closed maps, and supra homeomorphism maps are studied depending on the concept of supra R-open sets. Finally, new separation axioms are dened and their several properties are studied.

Downloads

Download data is not yet available.

References

T. M. Al-shami, On supra semi-open sets and some applications on topological spaces, Submitted.

R. Dev, S. Sampathkumar and M. Caldas, On α-open sets and sα-continuous maps, General Mathematics, 16(2008) 77-84.

A. Kar and P. Bhattacharyya, Some weak separation axioms, Bulletin of Calcutta Mathematical Society, 82(1990) 415-422.

A. S. Mashhour, A. A. Allam, F. S. Mahmoud and F. H. Kheder, On supra topological spaces, Indian Journal Pure and Applied Mathematics, 14(1983) 502-510.

J. M. Mustafa, Totally supra b-continuous and slightly supra b-continuous functions, Stud. University Babes-Bolyai Mathematics, 57(2012) 135-144.

J. M. Mustafa and H. A. Qoqazeh, Supra D-sets and associated separation axioms, European journal of Pure and Applied Mathematics, 80(2012) 657-663.

O. R. Sayed, Supra pre-open sets and supra pre-continuous on topological spaces, Series Mathematics and Information, 20(2010) 79-88.

O. R. Sayed and Takashi Noiri, On supra b-open sets and supra b-continuity on topological spaces, European journal of Pure and Applied Mathematics, 3(2010) 295-302.