On $(1,2)^{\star}-\check{g} $-closed sets in bitopological spaces

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DOI:

https://doi.org/10.26637/MJM0703/0016

Abstract

The aim of this paper, we introduce a new class of sets called $(1,2)^{\star}-\hat{g}_1$-closed sets, $(1,2)^{\star}-\mathscr{G}$-closed sets and $(1,2)^{\star}$-ğ-closed sets in bitopological spaces and we obtain several characterizations of this class and investigate the relationships with other some closed sets in bitopological spaces.

Keywords:

(1,2)^{\star}-\hat{\hat{g}} \text {-closed sets }, (1,2)^{\star}-\hat{g}_1 \text {-closed sets }, (1,2)^{\star}-\mathscr{G} \text {-closed sets and }(1,2)^{\star}-\check{g} \text {-closed sets }

Mathematics Subject Classification:

Mathematics
  • M. Ramaboopathi Department of Mathematics, The Madura College, Madurai District, Tamil Nadu, India.
  • K. M. Dharmalingam Department of Mathematics, The Madura College, Madurai District, Tamil Nadu, India.
  • Pages: 463-467
  • Date Published: 01-07-2019
  • Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)

J. Antony Rex Rodrigo, O. Ravi, A. Pandi and C. M. Santhana, On $(1,2)^{star}-s$-normal spaces and pre- $(1,2)^{star}-$ gs-closed functions, International Journal of Algorithms, Computing and Mathematics, 4(1)(2011), 29-42.

K. M. Dharmalingam and M. Ramaboopathi, New forms of generalized closed sets in bitopological spaces, Journal of Applied Science ans Computations, VI(III)(2019), 712718.

Z. Duszynski, M. Jeyaraman, M. S. Joseph, O. Ravi and M. L. Thivagar, A new generalization of closed sets in bitopology, South Asian Journal of Mathematics, 4(5)(2014), 215-224.

M. Garg, S. Agarwal and C. K. Goal, On $hat{hat{g}}-$ closed sets in topological spaces, Acta Ciencia Indica, XXXIII(4)M(2007), 1643-1652.

M. Garg, S. Khare and S. Agarwal, On ${ }^{star}$ g-closed sets in topological spaces, Ultra Science, 20(2)M(2008), 403416.

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

M. Lellis Thivagar, O. Ravi and M. E. Abd El-Monsef, Remarks on bitopological $(1,2)^{star}$-quotient mappings, $mathrm{J}$. Egypt Math. Soc., 16(1)(2008), 17-25.

${ }^{[8]} mathrm{N}$. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19(2)(1970), 89-96.

O. Ravi and M. L. Thivagar, Remarks on $lambda$-irresolute via $(1,2)^{star}$-sets, Advances App. Math. Analysis, 5(1)(2010), $1-15$.

O. Ravi, M. L. Thivagar and E. Ekici, Decomposition of $(1,2)^{star}$-continuity and complete $(1,2)^{star}$-continuity in bitopological spaces, Analele Universitatil Din Oradea. Fasc. Mathematical Tom XV(2008), 29-37.

O. Ravi, M. L. Thivagar and Jinjinli, Remarks on extensions of $(1,2)^{star}-g$-closed maps, Archimedes J. Math., $1(2)(2011), 177-187$.

D. Saravanakumar, N. Kalaivani and G. Sai Sundara Krishnan, On $tilde{mu}$-open sets in generalized topological spaces, Malaya J. Math., 3(3) (2015), 268-276.

D. Sekar and G. Kumar, On generalized $alpha$-regularinterior and generalized $alpha$-regular-closure topological spaces, Malaya J. Math., 5(1) (2017), 115-121.

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Published

01-07-2019

How to Cite

M. Ramaboopathi, and K. M. Dharmalingam. “On $(1,2)^{\star}-\check{g} $-Closed Sets in Bitopological Spaces”. Malaya Journal of Matematik, vol. 7, no. 03, July 2019, pp. 463-7, doi:10.26637/MJM0703/0016.