On Some Properties of β-Closed sets in topological spaces

International Journal of Mathematics Trends and Technology (IJMTT)
© 2017 by IJMTT Journal
Volume-42 Number-3
Year of Publication : 2017
Authors : Palanimani.P.G, Senthilvelavan.S


Palanimani.P.G, Senthilvelavan.S "On Some Properties of β-Closed sets in topological spaces ", International Journal of Mathematics Trends and Technology (IJMTT). V42(3):245-247 February 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

In this paper, the authors study the concept of properties a new class of closed sets called -closed sets (briefly -closed set). Also we investigate some of their properties.

[1] K.C.Chattopadhyay, O.Njastad and W.J.Thorn: Merotopic spaces and extensions of closurespaces, Can. J. Math.,(No 4)(1983), 613-629.
[2] K.C.Chattopadhyay and W.J.Thorn: Extensions of closure spaces, Can. J. Math.,(No 6) (1977), 1277-1286.
[3] G. Choquet, Sur les notions de filter et grille, ComptesRendusAcad.Sci.Paris, 224 (1947), 171-173.
[4] Dhananjoy Mandal and M.N. Mukherjee :On a type of generalized closed sets, Bol. Soc. Paran. Mat. (3s.) (2012); 67-76
[5] DimitrijeAndrijevic : On b-open sets, Mat. Vesnik 48 (1996), no.1-2, 59-64.
[6] N.Levine: Generalized closed sets in topology, Gent. Cire. Mat. Palermo, (2) 19 (1970) , 89-96.
[7] H. Maki, R.Devi and K. Balachandan: Associated topologies of generalized -closed sets and -generalized closed sets, Mem. Fac. Kochi Univ. Ser. A. Math., 15 (1994), 51-63.
[8] A.S. Mashhour, I.A. Hasanein and S.N. Ei-Deep : On precontinuous and weak precontinuous mappings, Proc. Math. And Phys.Soc. Egypt, 53 (1982), 47 – 53.
[9] O.Njastad: On some classes of nearly open sets, Pacific J. Math., 15 (1965) 961-970.
[10] T. Noiri: Almost g-closed functions and separation axioms, Acta. Math. Hungar., 82(3) (1999).
[11] B.Roy and M.N. Mukherjee: On a topology induced by a grill, Soochow J. Math. 33(4) (2007), 771-786.
[12] B.Roy and M.N. Mukherjee: Concerning topologies induces by principal grills, An. Stiint. Univ. AL. I. Cuzalasi. Mat. (N.S), 55 (2) (2009), 285-294.
[13] B.Roy and M.N. Mukherjee and S.K. Ghosh : On a subclass of preopen sets via grills: Stud. Si
[14] Cercet. Stiint. Ser. Mat. Univ. Bacau. 18 (2008), 255-266.
[15] W.J. Thorn: Proximity structures and grills, Math, Ann., 206 (1973), 35-62.
[16] P.G.Palanimani and R.Parimelazhagan, Normal ,Regularity and neibourhood in generalized β*closed maps, International journal of recent scientific research vol 3,issue 11,pp 968-971 nov 2012.

Closed sets, continous,neghbourhood