(1, 2)⋆-ψ-closed Sets
Keywords:
(1, 2)⋆-ψ-closed set, τ1,2-closed set, (1, 2)⋆-ˆ g-closed set, (1, 2)⋆-αsg-closed set, (1, 2)⋆-sg-open set
Abstract
In this paper, we introduce a new class of sets namely (1, 2)⋆-ψ-closed sets in bitopological spaces. This class lies between the class of τ1,2-closed sets and the class of (1, 2)⋆-ˆ g-closed sets. The notion of (1, 2)⋆-ψ-interior is defined and some of its basic properties are studied. Also we introduce the concept of (1, 2)⋆-ψ-closure in bitopological spaces using the notion of (1, 2)⋆-ψ-closed sets, and we obtain some related results. For any A ⊆ X, it is proved that the complement of (1, 2)⋆-ψ-interior of A is the (1, 2)⋆-ψ-closure of the complement of A.
References
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S.Jafari, M.Lellis Thivagar and Nirmala Mariappan, On (1, 2)⋆-αgˆ-closed sets, J. Adv. Math. Studies, 2(2)(2009), 25-34.
M.Lellis Thivagar, O.Ravi and M.E.Abd El-Monsef, Remarks on bitopological (1, 2)⋆-quotient mappings, J. Egypt Math. Soc., 16(1)(2008), 17-25.
N.Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19(2)(1970), 89-96.
O.Ravi and S.Ganesan, ¨ g-closed sets in topology, International Journal of Computer Science and Emerging Technologies, 2(2011), 330-337.
O.Ravi and S.Ganesan, (1, 2)⋆-g¨α-closed sets in bitopology, (submitted).
O.Ravi, M.Kamaraj, A.Pandi and K.Kumaresan, (1, 2)⋆-g¨-closed and (1, 2)⋆-g¨-open maps in bitopological spaces, International Journal of Mathematical Archive, 3(2)(2012), 586-594.
O.Ravi, M.L.Thivagar and A.Nagarajan, (1, 2)⋆-αg-closed sets and (1, 2)⋆-gα-closed sets, (submitted).
O.Ravi and M.Lellis Thivagar, A bitopological (1, 2)⋆-semi-generalized continuous maps, Bull. Malays. Math. Sci. Soc., (2), 29(1)(2006), 79-88.
O.Ravi and M.Lellis Thivagar, On stronger forms of (1, 2)⋆-quotient mappings in bitopological spaces, Internat. J. Math. Game Theory and Algebra., 14(6) (2004), 481-492.
O.Ravi, S.Pious Missier and T.Salai Parkunan, On bitopological (1, 2)⋆-generalized homeomorphisms, Int J. Contemp. Math. Sciences., 5(11)(2010), 543-557.
O.Ravi, M.L.Thivagar and Jinjinli, Remarks on extensions of (1, 2)⋆-g-closed maps, Archimedes J. Math., 1(2)(2011), 177-187.
O.Ravi and M.L.Thivagar, Remarks on λ-irresolute functions via (1, 2)⋆-sets, Advances in App. Math. Analysis, 5(1)(2010), 1-15.
O.Ravi, M.L.Thivagar and E.Hatir, Decomposition of (1, 2)⋆-continuity and (1, 2)⋆-α-continuity, Miskolc Mathematical Notes., 10(2)(2009), 163-171.
M.Sheik John, A study on generalizations of closed sets and continuous maps in topological and bitopological spaces, Ph. D Thesis, Bharathiar University, Coimbatore, (2002).
M.K.R.S.Veera kumar, ˆ g-closed sets in topological spaces, Bull. Allah. Math. Soc., 18(2003), 99-112.
S.Jafari, M.Lellis Thivagar and Nirmala Mariappan, On (1, 2)⋆-αgˆ-closed sets, J. Adv. Math. Studies, 2(2)(2009), 25-34.
M.Lellis Thivagar, O.Ravi and M.E.Abd El-Monsef, Remarks on bitopological (1, 2)⋆-quotient mappings, J. Egypt Math. Soc., 16(1)(2008), 17-25.
N.Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19(2)(1970), 89-96.
O.Ravi and S.Ganesan, ¨ g-closed sets in topology, International Journal of Computer Science and Emerging Technologies, 2(2011), 330-337.
O.Ravi and S.Ganesan, (1, 2)⋆-g¨α-closed sets in bitopology, (submitted).
O.Ravi, M.Kamaraj, A.Pandi and K.Kumaresan, (1, 2)⋆-g¨-closed and (1, 2)⋆-g¨-open maps in bitopological spaces, International Journal of Mathematical Archive, 3(2)(2012), 586-594.
O.Ravi, M.L.Thivagar and A.Nagarajan, (1, 2)⋆-αg-closed sets and (1, 2)⋆-gα-closed sets, (submitted).
O.Ravi and M.Lellis Thivagar, A bitopological (1, 2)⋆-semi-generalized continuous maps, Bull. Malays. Math. Sci. Soc., (2), 29(1)(2006), 79-88.
O.Ravi and M.Lellis Thivagar, On stronger forms of (1, 2)⋆-quotient mappings in bitopological spaces, Internat. J. Math. Game Theory and Algebra., 14(6) (2004), 481-492.
O.Ravi, S.Pious Missier and T.Salai Parkunan, On bitopological (1, 2)⋆-generalized homeomorphisms, Int J. Contemp. Math. Sciences., 5(11)(2010), 543-557.
O.Ravi, M.L.Thivagar and Jinjinli, Remarks on extensions of (1, 2)⋆-g-closed maps, Archimedes J. Math., 1(2)(2011), 177-187.
O.Ravi and M.L.Thivagar, Remarks on λ-irresolute functions via (1, 2)⋆-sets, Advances in App. Math. Analysis, 5(1)(2010), 1-15.
O.Ravi, M.L.Thivagar and E.Hatir, Decomposition of (1, 2)⋆-continuity and (1, 2)⋆-α-continuity, Miskolc Mathematical Notes., 10(2)(2009), 163-171.
M.Sheik John, A study on generalizations of closed sets and continuous maps in topological and bitopological spaces, Ph. D Thesis, Bharathiar University, Coimbatore, (2002).
M.K.R.S.Veera kumar, ˆ g-closed sets in topological spaces, Bull. Allah. Math. Soc., 18(2003), 99-112.
How to Cite
S.Saranya, N.Seenivasagan, & O.Ravi. (2017). (1, 2)⋆-ψ-closed Sets. International Journal of Current Research in Science and Technology, 3(8), 1-10. Retrieved from https://crst.gfer.org/index.php/crst/article/view/93
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