g_*^*-I-Closed Sets and Their Properties in in Ideal Topological Space
Abstract
There are many research papers that deal with different types of generalized closed sets. Levine [4] introduced generalized closed (briefly, -closed) sets and studied their basic properties and Veera Kumar [5] introduced -closed sets in topological spaces. The purpose of this present paper is to define a new class of generalized idea closed sets called -closed sets by using -open set .In this paper, we introduce the -closed sets, characterizations and properties of -closed sets and its complement and other related sets. We prove that the class of closed sets lies between the class of -closed sets and the class of -closed sets. Also, we find some relations between -closed sets and already existing closed sets. -open neighborhood is introduced and their properties are investigated.
References
- and V. V. Pauline Mary Helen M, Ponnuthai Selvarani,( 2012) g**- closed sets in topological spaces, J. Math. Arch., vol. 3, no. 5.
- Dontchev, M. Ganster, and T. Noiri, (1999 )Unified operation approach of generalized closed sets via topological ideals, Math. Jpn., vol. 49, pp. 395402.
- Jankovi and T. R. Hamlett, (1990 )New topologies from old via ideals, Am. Math. Mon., vol. 97, no. 4, pp. 295310.
- Kuratowski,(1966.)Topology. Academic Press, Vol. 1. NewYork.
- L. Newcomb, (1967 )Topologies which are compact modulo an ideal, Ph. D. Diss. Univ. Cal. St. Barbar..
- Levine, (1963 )Semi-open sets and semi-continuity in topological spaces, Am. Math. Mon., vol. 70, no. 1, pp. 3641.
- Levine, (1970 )Generalized closed sets in topology, Rend. del Circ. Mat. di Palermo, vol. 19, pp. 8996.
- M. Khan and T. Noiri, (2010 )On gI-closed sets in ideal topological spaces, Adv. Stud. Topol., vol. 1, pp. 2933.
- Navaneethakrishnan and J. Paulraj Joseph, (2008 )g-Closed sets in ideal topological spaces, Acta Math. Hungarica, vol. 119, no. 4, pp. 365371.
- R. Devi, D. Sivaraj, and T. T. Chelvam, (2005 )Codense and completely codense ideals., Acta Math. Hungarica, vol. 108, no. 3.
- V Rancin,( 1973) Compactness modulo an ideal, in Soviet Mathematics Doklady, vol. 13, pp. 193197.
- V. Kumar,( 2006) Between g*-Closed Sets in Topological Spaces, Antarct. J. Math., vol. 3, no. 1, pp. 4365.
- Vaidyanathaswamy,( 1960.) Set topology. Chelsea Publishing Company.
- Y. R. Vaidyanathaswamy, (1945 )The Localization theory in set-topology, Proc. Indian Acad. Sci., vol. 20, pp. 5161.
