A decomposition of pairwise continuity via ideals

  • Takashi Noiri Yatsushiro College of Technology
  • M. Rajamani NGM College
  • M. Maheswari NGM College

Abstract

In this paper, we introduce and study the notions of (i, j) - regular - ℐ -closed sets, (i, j) - Aℐ -sets, (i, j) - ℐ -locally closed sets, p- Aℐ -continuous functions and p- ℐ -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.

Downloads

Download data is not yet available.

Author Biographies

Takashi Noiri, Yatsushiro College of Technology
Shiokita-cho, Hinagu, Yatsushiro-shi
M. Rajamani, NGM College

Department of Mathematics

M. Maheswari, NGM College

Department of Mathematics

References

M. E. Abd El-Monsef, E. F. Lashien and A. A. Nasef, On I-open sets and I-continuous functions, Kyungpook Math. J., 32(1992), 21-30.

J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, arXiv:Math/9901017v1 5 Jan. 1999(Internet).

B. Dvalishvili, On dimension and some other problems of bitopological spaces, Trudi Tbil. Math. Instituta, T.LVI(1977), 15-52.

E. Hatir and T. Noiri, On decompositions of continuity via idealization, Acta Math. Hungar., 96(4)(2002), 341-349.

E. Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205-215.

D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(1990), 295-310.

D. Jankovic and T. R. Hamlett, Compatible extension of ideals, Boll. U. M. I., (7)6-B(3)(1992), 453-465.

M. Jelic, A decomposition of pairwise continuity, J. Inst. Math. Comput. Sci. Math, Ser. 3(1990), 25-29.

J. Kelly, Bitopological spaces, Proc. London Math. Soc., 13(1963), 71-89.

A. Keskin, T. Noiri and S. Yuksel, Idealization of a decomposition theorem, Acta Math. Hungar., 102(4)(2004), 269-277.

K. Kuratowski, Topology, Vol. I, Academic Press, New York, (1966).

S. N. Maheshwari and R. Prasad, Semi-open sets and semi-continuous function in bitopological spaces, Math Notae, 26 (1977-78), 29-37.

W. J. Pervin, Connectedness in bitopological spaces, Indag. Math. 29 (1967), 369-372.

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.

S. Sampath Kumar, On decomposition of pairwise continuity, Bull. Cal. Math. Soc. 89 (1997), 441-446.

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.

R. Vaidyanathaswamy, The localisation theory in set topology, Proc. Indian Acad. Sci. 20(1945), 51-61.

R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Company, New York, 1960.

Published
2015-02-16
Section
Articles