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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 1 | Year 2018 | Article Id. IJMTT-V57P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P509

Generalized Pre Closed Sets with Respect to an Ideal


V.Senthilkumaran, R.Krishnakumar, Y.Palaniappan
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 sets was introduced by Levine. In this paper, we introduce and investigate the concept of pre generalized closed sets with respect to an ideal.

Keywords
Topological spaces, pre generalized closed set, ideal.
References

[1] T.R.Hamlett and D.Jankovic, Compactness with respect to an ideal, Boll.Un.Mat.Ita., (7), 4-B, 849-861, 1990.
[2] T.R.Hamlett and D.Jankovic, Ideals in topological spaces and the set operator, Boll.Un.Mat.Ita., 7,863-874,1990
[3] T.R.Hamlett and D.Jankovic, Ideals in General Topology and Applications (Middletown, CT, 1988), 115-125, Lecture Notes in Pure and Appl. Math.Dekker, New York, 1990.
[4] T.R.Hamlett and D.Jankovic, Compatible extensions of ideals, Boll.Un.Mat.Ita., 7,453- 465, 1992.
[5]S.Jafari and N.Rajesh, Generalized closed sets with respect to an ideal,European Journal of Pure and Applied Mathematics,Vol 4,No 2,147-151,2011
[6]D.Jankovic and T.R.Hamlett, New topologies via ideals, Amer.Math.Month., 97,295- 310, 1990.
[7]K.Kuratowski, Topologies I,Warszawa
[8]N.Levine, Generalized closed sets in topology, Rend. Circ.Mat.Palermo, 19(2), 89-96, 1970
[9]R.L.Newcomb, Topologies which are compact modulo an ideal, Ph.D., Dissertation,Univ.Cal. at Santa Barbara,1967
[10] D.V Rancin, Compactness modulo an ideal, Soviet Math.Dokl., 13,193-197, 1972
[11]P.Samuels, A topology from a given topology and ideal, J.London Math. Soc. (2) (10) 409-416, 1975.

Citation :

V.Senthilkumaran, R.Krishnakumar, Y.Palaniappan, "Generalized Pre Closed Sets with Respect to an Ideal," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 1, pp. 63-66, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P509

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