π-Generalized Closed Sets with Respect to an Ideal
Keywords:
Topological space, π-open set, π-generalized closed set, g-closed set, Ig-closed set, Iπg-closed set, ideal
Abstract
An ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under finite unions. The concept of generalized closed (g-closed) sets was introduced by Levine [16]. Quite Recently, Jafari and Rajesh [12] have introduced and studied the notion of generalized closed (g-closed) sets with respect to an ideal. Many variations of g-closed sets are being introduced and investigated by modern researchers. One among them is πg-closed sets which were introduced by Dontchev and Noiri [4]. In this paper, we introduce and investigate the concept of π-generalized closed (πg-closed) sets with respect to an ideal.
References
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V.Zaitsev, On certain classes of topological spaces and their bicompactifications, Dokl. Akad. Nauk. SSSR, 178(1968), 778-779.
G.Aslim, A.Cakshu Guler and T.Noiri, On πgs-closed sets in topological spaces, Acta Math. Hungar., 112(4)(2004), 275-283.
M.Caldas, S.Jafari, K.Viswanathan and S.Krishnaprakash, On contra πgp-continuous functions, Kochi J. Math., 5(2010), 67-78.
J.Dontchev and T.Noiri, Quasi-normal spaces and πg-closed sets, Acta Math. Hungar., 89(3)(2000), 211-219.
E.Ekici, On contra πg-continuous functions, Chaos Solitons and Fractals, 35(2008), 71-81.
E.Ekici and C.W.Baker, On πg-closed sets and continuity, Kochi J. Math., 2(2007), 35-42.
E.Ekici, On (g, s)-continuous and (πg, s)-continuous functions, Sarajevo J. Math., 3(15)(2007), 99-113.
T.R.Hamlett and D.Jankovic, Compactness with respect to an ideal, Boll. Un. Mat. Ita., 7 (4-B)(1990), 849-861.
T.R.Hamlett and D.Jankovic, Ideals in topological spaces and the set operator, Boll. Un. Mat. Ita., 7(1990), 863-874.
T.R.Hamlett and D.Jankovic, Ideals in General Topology and Applications (Midletown, CT, 1988), Lecture Notes in Pure and Appl. Math. Dekker, New York, (1990), 115-125.
T.R.Hamlett and D.Jankovic, Compatible extensions of ideals, Boll. Un. Mat. Ita., 7(1992), 453-465.
S.Jafari and N.Rajesh, Generalized closed sets with respect to an ideal, European J. Pure Appl. Math., 4(2)(2011), 147-151.
D.Jankovic and T.R.Hamlett, New topologies from old via ideals, Amer. Math. Month., 97(1990), 295-310.
L.N.Kalantan, π-normal topological spaces, Filomat., 22(1)(2008), 173-181.
K.Kuratowski, Topologies I, Warszawa, (1933).
N.Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo., 19(2)(1970), 89-96.
R.L.Newcomb, Topologies which are compact modulo an ideal, Ph.D. Dissertation, Univ. Cal. at Santa Barbara, (1967).
D.V.Rancin, Compactness modulo an ideal, Soviet Math. Dokl., 13(1972), 193-197.
P.Samuels, A topology from a given topology and ideal, J. London Math. Soc., (2)(10)(1975), 409-416.
M.H.Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375-481.
S.Takigawa and H.Maki, Every nonempty open set of the digital n-space is expressible as the union of finitely many nonempty regular open sets, Sci. Math. Jpn., 67(2008), 365-376.
V.Zaitsev, On certain classes of topological spaces and their bicompactifications, Dokl. Akad. Nauk. SSSR, 178(1968), 778-779.
How to Cite
O. Ravi, M. Suresh, & A. Pandi. (2015). π-Generalized Closed Sets with Respect to an Ideal. International Journal of Current Research in Science and Technology, 1(5), 53-58. Retrieved from https://crst.gfer.org/index.php/crst/article/view/28
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