A decomposition of pairwise continuity via ideals
DOI:
https://doi.org/10.5269/bspm.v34i1.14611Abstract
In this paper, we introduce and study the notions of (i, j) - regular - â„ -closed sets, (i, j) - Aâ„ -sets, (i, j) - â„ -locally closed sets, p- Aâ„ -continuous functions and p- â„ -LC-continuous functions in ideal bitopological spaces and investigate some of their properties. Also, a new decomposition of pairwise continuity is obtained using these sets.
References
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14. M. Rajamani, V. Inthumathi and M. Maheswari, Decompositions of pairwise continuity in ideal bitopological spaces, J. Adv. Res. Pure Math., 4(3) (2012), 8-18.
15. S. Sampath Kumar, On decomposition of pairwise continuity, Bull. Cal. Math. Soc. 89 (1997), 441-446.
16. P. Sundaram and M. Rajamani, Another Decomposition of pairwise continuity, Proc. of the Annual Conference of KMA and International Seminar on Mathematics Tradition of Kerala, St. Dominic’s College, Kanjirapally, Jan. 17-19(2000), 70-71.
17. R. Vaidyanathaswamy, The localisation theory in set topology, Proc. Indian Acad. Sci. 20(1945), 51-61.
18. R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Company, New York, 1960.
2. J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, arXiv:Math/9901017v1 5 Jan. 1999(Internet).
3. B. Dvalishvili, On dimension and some other problems of bitopological spaces, Trudi Tbil. Math. Instituta, T.LVI(1977), 15-52.
4. E. Hatir and T. Noiri, On decompositions of continuity via idealization, Acta Math. Hungar., 96(4)(2002), 341-349.
5. E. Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205-215.
6. D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(1990), 295-310.
7. D. Jankovic and T. R. Hamlett, Compatible extension of ideals, Boll. U. M. I., (7)6-B(3)(1992), 453-465.
8. M. Jelic, A decomposition of pairwise continuity, J. Inst. Math. Comput. Sci. Math, Ser. 3(1990), 25-29.
9. J. Kelly, Bitopological spaces, Proc. London Math. Soc., 13(1963), 71-89.
10. A. Keskin, T. Noiri and S. Yuksel, Idealization of a decomposition theorem, Acta Math. Hungar., 102(4)(2004), 269-277.
11. K. Kuratowski, Topology, Vol. I, Academic Press, New York, (1966).
12. S. N. Maheshwari and R. Prasad, Semi-open sets and semi-continuous function in bitopological spaces, Math Notae, 26 (1977-78), 29-37.
13. W. J. Pervin, Connectedness in bitopological spaces, Indag. Math. 29 (1967), 369-372.
14. M. Rajamani, V. Inthumathi and M. Maheswari, Decompositions of pairwise continuity in ideal bitopological spaces, J. Adv. Res. Pure Math., 4(3) (2012), 8-18.
15. S. Sampath Kumar, On decomposition of pairwise continuity, Bull. Cal. Math. Soc. 89 (1997), 441-446.
16. P. Sundaram and M. Rajamani, Another Decomposition of pairwise continuity, Proc. of the Annual Conference of KMA and International Seminar on Mathematics Tradition of Kerala, St. Dominic’s College, Kanjirapally, Jan. 17-19(2000), 70-71.
17. R. Vaidyanathaswamy, The localisation theory in set topology, Proc. Indian Acad. Sci. 20(1945), 51-61.
18. R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Company, New York, 1960.
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2015-02-16
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