Volume 53 | Number 7 | Year 2018 | Article Id. IJMTT-V53P564 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P564
In 2012 Sekar and Jayakumar introduced and investigated a new class of sets and functions between supra topological spaces called supra I - open sets and supra I - continuous functions respectively. In this paper we newly originate the notions of supra I - compact spaces, supra I -Lindelof spaces, countably supra I - compact spaces and supra I - connected spaces. We also interpret their several effects and characterizations.
1. Abl El-Monsef, M. E. El -Deeb S. N. Mahmoud, R. A.: β-open sets and β-continuous mappings. Bull. Fac. Sci. Assint Univ., 12, pp. 77 – 90, 1983.
2. Abl El – Monsef, M. E., Ramadan, A. E.: On fuzzy supra topological space. Indian J. Pure and Appl. Math. 4 (18), pp. 322 – 329, 1987.
3. D. Andrijevic, On b-open sets, Mat. Vesnik, 48 (1996), no.1-2, pp. 59-64.
4. C. W. Baker, Contra somewhat continuous functions, Missouri J. Math. Sci., 27(2015), pp. 1 – 8.
5. C. W. Baker, Somewhat Open Sets, Gen. Math. Notes, Vol. 34, No. 1, May 2016, pp. 29 – 36.
6. S. Balasubramanian, C. Sandhya and P.A.S. Vyjayanthi, On ν−compact spaces, Scientia Magna, 5(1) (2009), pp. 78 – 82.
7. Miguel Caldas, Saeid Jafari, and Raja M. Latif: “b – Open Sets and A New Class of Functions”, Pro Mathematica, Peru, Vol. 23, No. 45 – 46, pp. 155 – 174, (2009).
8. S. G. Crossley and S. K. Hildebrand, Semi-closure, Texas J. Sci., 22(1971), pp. 99 – 112.
9. R. Devi, S. Sampathkumar and M. Caldas, On supra α open sets and S-continuous maps, General Mathematics, 16 (2), (2008), pp. 77 – 84.
10. C. Duraisamy and R. Vennila, Somewhat λ-Continuous Functions, Applied Mathematical Sciences, Vol. 6, 2012, no. 39, pp. 1945 - 1953
11. K. R. Gentry and H. B. Hoyle, Somewhat continuous functions, Czechslovak Math. J., 21 (96) (1971), pp. 5 – 12. doi:Zbl 0222.54010.
12. H. Z. Hdeib, ω-closed mappings, Rev. Colomb. Mat., 16 (1-2) (1982), pp. 65 – 78.
13. Jamal M. Mustafa, Supra b – compact and supra b – Lindelof spaces, Journal of Mathematics and Applications, 36, (2013), pp. 79 – 83.
14. K. Krishnaveni and M. Vigneshwaran, Some Stronger forms of supra bTμ - continuous function, Int. J. Mat. Stat. Inv., 1(2), (2013), pp. 84 – 87.
15. K. Krishnaveni and M. Vigneshwaran, On bTμ -Closed sets in supra topological Spaces, Int. J. Mat. Arc., 4(2), (2013), pp. 1 – 6.
16. K. Krishnaveni and M. Vigneshwaran, bTμ- compactness and bTμ - connectedness in supra topological spaces, European Journal of Pure and Applied Mathematics, Vol. 10, No. 2, 2017, pp. 323 – 334 ISSN 1307-5543 – www.ejpam.com.
17. Raja M. Latif, On Characterizations of Mappings, Soochow Journal of Mathematics, Volume , No. 4, pp. 475 – 495. 1993.
18. Raja M. Latif, On Semi-Weakly Semi-Continuous Mappings, Punjab University Journal of Mathematics, Volume XXVIII, (1995), pp. 22 – 29,
19. Raja M. Latif, Characterizations and Applications of Gamma-Open Sets, Soochow Journal of Mathematics, (Taiwan), Vol. 32, No. 3, pp. 369 – 378. (July, 2006).
20. Raja M. Latif, Characterizations of Mappings in Gamma-Open Sets, Soochow Journal of Mathematics, (Taiwan), Vol. 33, No. 2, (April 2007), pp. 187 – 202.
21. Raja M. Latif, Raja M. Rafiq, and M. Razaq, Properties of Feebly Totally Continuous Functions in Topological Spaces, UOS. Journal of Social Sciences & Humanities (UOSJSSH), ISSN # Print:2224-2341. Special Edition 2015, pp.72 – 84.
22. Raja M. Latif, Characterizations of Feebly Totally Open Functions, “Advances in Mathematics and Computer Science and their Applications, (2016) pp. 217 – 223.
23. Raja M. Latif, Alpha – Weakly Continuous Mappings in Topological Spaces, “International Journal of Advanced Informa tion Science and Technology (IJAIST), ISSN # 231 9:2682 Vol. 51, No, 51, July 2016. pp. 12 – 18.
24. N. Levine, A decomposition of continuity in topological spaces, Amer. Math. Monthly, 68(1961), pp. 44– 46 .
25. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), pp. 36 - 41.
26. T. Noiri, On δ-continuous functions, J. Korean Math. Soc., 16(1980), pp. 161 – 166.
27. T. Noiri and N. Rajesh, Somewhat b-continuous functions, J. Adv. Res. in Pure Math., 3(3) (2011), pp. 1 – 7.
28. Marwan A. Jardo, Supra i – Open Sets and Supra i – continuity on Topological Spaces, International Journal of Scientific & Engineering Research, Volume 7, Issue 10 (2016), pp. 108 – 110.
29. A. S. Mashhour, A. A. Allam, F. S. Mohamoud and F. H. Khedr, On supra topological spaces, Indian J. Pure and Appl. Math., No.4, 14(1983), pp. 502 – 510.
30. P. G. Patil, w - compactness and w - connectedness in topological spaces, Thai. J. Mat., (12), (2014), pp. 499 – 507.
31. A. Robertand S. Pious Missier, On Semi*-Connected and Semi*-Compact Spaces, International Journal of Modern Engineering Research, Vol. 2, Issue 4, July – Aug. 2012, pp. 2852 – 2856.
32. O. R. Sayed, Takashi Noiri.: On supra b – open set and supra b – continuity on topological spaces. European Journal of pure and applied Mathematics, 3(2), pp. 295 – 302, 2010.
33. S. Sekar and P. Jayakumar, On Supra I – Open Sets and Supra I – Continuous Functions, International Journal Scientific and Engineering Research, Vol. 3, Issue 5, May 2012, pp. 01 – 03.
34. L. A. Steen and J. A. Seebach Jr, Counterexamples in Topology, Holt, Rinenhart and Winston, New York 1970.
35. N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl., 78(2) (1968), pp.103 – 118.
36. K. Al-Zoubi and B. Al-Nashef, The topology of ω-open subsets, Al-Manarah, IX (2) (2003), pp. 169 - 179.
36. Albert Wilansky, Topology for Analysis, Devore Publications, Inc, Mineola New York. (1980).
37. Stephen Willard, General Topology, Reading, Mass.: Addison Wesley Pub. Co. (1970).
38. Stephen Willard and Raja M. Latif, Semi-Open Sets and Regularly Closed Sets in Compact Metric Spaces, Mathematica Japonica, Vol. 46, No.1, pp. 157 – 161, 1997.
Raja Mohammad Latif, "Supra – I– Compactness and Supra – I – Connectedness," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 7, pp. 525-538, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P564