New Types of Generalized locally Closed Sets
Keywords:
Topological space, g-closed set, g⋆-closed set, g⋆-lc⋆ set, g⋆-lc⋆⋆ set
Abstract
The aim of this paper is to introduce and study the classes of g⋆-locally closed sets, g⋆-lc⋆ sets and g⋆-lc⋆⋆ sets which are weaker forms of the class of locally closed sets. Furthermore the relations with other notions connected with the forms of locally closed sets are investigated.
References
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J.Dontchev, On submaximal spaces, Tamkang J. Math., 26(1995), 253-260.
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O.Ravi, Properties of g⋆-closed sets, Preprint.
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M.H.Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 374-481.
M.K.R.S.Veera Kumar, ˆ g-locally closed sets and GˆLC-functions, Indian J. Math., 43(2)(2001), 231-247.
M.K.R.S.Veera Kumar, Between closed sets and g-closed sets, Mem. Fac. Sci. Kochi. Univ. Ser. A. Math., 21(2000), 1-19.
P.Bhattacharyya and B.K.Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29(3)(1987), 375-382.
N.Bourbaki, General topology, Part I, Addison-Wesley, Reading, Mass., (1966).
S.G.Crossley and S.K.Hildebrand, Semi-closure, Texas J. Sci., 22(1971), 99-112.
J.Dontchev, On submaximal spaces, Tamkang J. Math., 26(1995), 253-260.
M.Ganster and I.L.Reilly, Locally closed sets and LC-continuous functions, Internat J. Math. Math. Sci., 12(3)(1989), 417-424.
Y.Gnanambal, Studies on generalized pre-regular closed sets and generalization of locally closed sets, Ph.D Thesis, Bharathiar University, Coimbatore, (1998).
N.Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19(2)(1970), 89-96.
N.Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
N.Palaniappan and K.C.Rao, Regular generalized closed sets, Kyungpook Math. J., 33(1993), 211-219.
J.H.Park and J.K.Park, On semi-generalized locally closed sets and SGLC-continuous functions, Indian J. Pure Appl. Math., 31(9)(2000), 1103-1112.
O.Ravi, Properties of g⋆-closed sets, Preprint.
A.H.Stone, Absolutely FG spaces, Proc. Amer. Math. Soc., 80(1980), 515-520.
M.H.Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 374-481.
M.K.R.S.Veera Kumar, ˆ g-locally closed sets and GˆLC-functions, Indian J. Math., 43(2)(2001), 231-247.
M.K.R.S.Veera Kumar, Between closed sets and g-closed sets, Mem. Fac. Sci. Kochi. Univ. Ser. A. Math., 21(2000), 1-19.
How to Cite
O. Ravi, M. Kamaraj, S. Murugambigai, & A. Pandi. (2015). New Types of Generalized locally Closed Sets. International Journal of Current Research in Science and Technology, 1(6), 1-10. Retrieved from https://crst.gfer.org/index.php/crst/article/view/29
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