On T1 T2-g-Open Sets in Bitopological Spaces

Main Article Content

K. Vithyasangaran
P. Elango
S. Sathaananthan
J. Sriranganesan
P. Paramadevan

Abstract

In this paper, we introduced and studied a new kind of generalized open set called τ1τ2-g-open set in a bitopological space (X, τ1, τ2). The properties of this τ1τ2-g-open set are studied and compared with some of the corresponding generalized open sets in general topological spaces and bitopological spaces. We also dened the τ1τ2-g-continuous function and studied some its properties.

Keywords:
Generalized open sets, bitopological spaces, continuous maps.

Article Details

How to Cite
Vithyasangaran, K., Elango, P., Sathaananthan, S., Sriranganesan, J., & Paramadevan, P. (2019). On T1 T2-g-Open Sets in Bitopological Spaces. Journal of Advances in Mathematics and Computer Science, 34(2), 1-8. https://doi.org/10.9734/jamcs/2019/v34i230216
Section
Original Research Article

References

Kelly JC. Bitopological Spaces. Proc. London Math Soc. 1963;13:71-89.

Levine N. Generalized closed sets in topology. Rend. Circlo. Mat. Palermo. 1970;13(2):89-96.

Bhattacharyya P, Lahiri BK. Semi-generalized closed sets in topology. Indian J. Math. 1987;29:376-382.

Maki H, Devi R, Balachandran K. Generalized α-closed sets in topology. Bull. Fukuoka Univ. Ed., Part-III. 1993;42:13-21.

Keskin A, Noiri T. On bD-sets and associated separation axioms. Bull. Iran. Math. Soc. 2009;35(1):179-198.

Stone M. Application of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc. 1937;41:374-481.

Sundaram P, Shrik John M. On ω-closed sets in topology. Acta Ciencia Indica. 2000;4:389-392.

Crossley G, Hildebrand SK. Semi-closure. Texas J. Sci. 1971;22:99-112.

Njastad O. On some classes of nearly open sets. Pacic. J. Math. 1965;15:961-970.

Vithyasangaran K, Elango P. On τ1τ2-g-Closed Sets in Bitopological Spaces. Asian Research Journal of Mathematics. 2018;11(2):1-8.

Arya SP, Nour T. Characterizations of S-normal spaces. Indian J. Pure. Appl. MAth. 1990;21(8):717-719.

Palaniappan N, Rao KC. Regular generalized closed sets. Kyungpook Math. 1993;33:211-219.

Maki H, Devi R, Balachandran K. Associate topologies of generalized α-closed sets and α- Generalized Closed Sets. Mem. Fac. Kochi Univ. Ser. A. Math. 1994;15:51-63.

Maki H, Umehara J, Noiri T. Every topological space is pre-T1

Mem. Fac. Sci. Kochi Univ. Math. 1996;17:33-42.

Dontchev J. On generalizing semi-preopen sets. Mem. Fac Sci. Kochi. Univ. Ser. A. Math. 1995;16:35-48.

Vijaya Priya V, Indira T. On regular generalized B♯-closed sets. Annals of Pure and Applied Mathematics. 2017;14(3):371-377.

Lellis Thivagar M. Meera Devi B, Hatir E. δ^g-closed sets in topological spaces. Gen. Math. Notes. 2010;1(2):17-25.

Pauline Mary Helen M, Kulandhai Therese A. (gsp)-closed sets in topological spaces.

International Journal of Mathematical Trends and Technology (IJMTT). 2014;6:75-86.

Veera Kumar MKRS. ^g-closed sets in topologycal spaces. Bull. Allah. Math. Soc. 2003;18:99- 112.

Fukutake T. On generalized closed sets in bitopological Spaces. Acta Ciencia of Educ. 1985;35:19-28.

Fukutake T. Semi open sets on bitopological spaces. Bull. Fukuoka. Univ. of Educ. 1989;38:1-7.

Indira T. τ1τ2