On Some Maps in Supra Topological Ordered Spaces

Abstract

In [6] the notion of supra semi open sets was presented and some of its properties were discussed. In this study, we introduce and investigate four main concepts namely supra continuous (supra open, supra closed, supra homeomorphism) maps via supra topological ordered spaces. Our findings in this work generalize some previous results in ([1], [13]). Many examples are considered to show the concepts introduced and main results obtained herein.

Keywords

• Ordered supra semi separation axioms.

References

1. [1] M. Abo-elhamayel and T. M. Al-shami, Supra homeomorphism in supra topological ordered spaces, Facta Universitatis, Series: Mathematics and Informatics, 31 (5) (2016) 1091-1106.
2. [2] T. M. Al-shami, Some results related to supra topological spaces, Journal of Advanced Studies in Topology, 7 (4) (2016) 283-294.
3. [3] T. M. Al-shami, Utilizing supra ®-open sets to generate new types of supra compact and supra LindelÄof spaces, Facta Universitatis, Series: Mathematics and Informatics, 32 (1) (2017) 151-162.
4. [4] T. M. Al-shami, Somewhere dense sets and ST1-spaces, Punjab University Journal of Mathematics, 49 (2) (2017) 101-111.
5. [5] T. M. Al-shami, Supra ¯-bicontinuous maps via topological ordered spaces, Mathematical Sciences Letters, 6 (3) (2017) 239-247.
6. [6] T. M. Al-shami, On supra semi open sets and some applications on topological spaces, Journal of Advanced Studies in Topology, 8(2) (2017) 144-153.
7. [7] T. M. Al-shami and M. K. Tahat, I (D, B)-supra pre maps via supra topological ordered spaces, Journal of Progressive Research in Mathematics, 12 (3) (2017) 1989-2001.
8. [8] S. D. Arya and K. Gupta, New separation axioms in topological ordered spaces, Indain Journal Pure and Appllied Mathematics, 22 (1991) 461-468.

9. [9] P. Das, Separation axioms in ordered spaces, Soochow Journal of Mathematics, 30 (4) (2004) 447-454.
10. [10] M. E. El-Shafei, M. Abo-elhamayel and T. M. Al-shami, On supra R-open sets and some applications on topological spaces, Journal of Progressive Research in Mathematics, 8 (2) (2016) 1237-1248.
11. [11] M. E. El-Shafei, M. Abo-elhamayel and T. M. Al-shami, Strong separation axioms in supra topological ordered spaces, Mathematical Sciences Letters, 6 (3) (2017) 271-277.
12. [12] M. E. El-Shafei, M. Abo-elhamayel and T. M. Al-shami, Supra R-homeomorphism in supra topological ordered spaces, International Journal of Algebra and Statistics, 6 (1-2) (2017) 158-167.
13. [13] M. E. El-Shafei, M. Abo-elhamayel and T. M. Al-shami, Generating ordered maps via supra topological ordered spaces, International Journal of Modern Mathematical Sciences, 15 (3) (2017) 339-357.
14. [14] M. K. R. S. V. Kumar, Homeomorphism in topological ordered spaces, Acta Ciencia Indian, XXVIII(M)(1)(2002) 67-76.
15. [15] N. Levine, Semi-open sets and semi-continuity in topological spaces, American Mathematical Society, 70 (1963) 36-41.
16. [16] A. S. Mashhour, A. A. Allam, F. S. Mahmoud and F. H. Khedr, On supra topological spaces, Indain J. Pure Appl. Math, 14 (4) (1983) 502-510.
17. [17] S. D. McCartan, Separation axioms for topological ordered spaces, Mathematical Proceedings of the Cambridge Philosophical Society, 64 (1986) 965-973.
18. [18] L. Nachbin, Topology and ordered, D. Van Nostrand Inc. Princeton, New Jersey, (1965).