δ(δg)* - Sets and Functions in Topological Spaces

  • Meriam Niepes Bitasolo BISU-Calape Campus
Keywords: Keywords: δ(δg)* - set, δ(δg)* - closure, δ(δg)*-continuous functions, absolute-δ(δg)* - continuous functions, rs - δ(δg)* - continuous functions

Abstract

This study introduced the notion of delta(delta g)star set and functions in topological spaces (briefly TS). This proves that in TS, the delta-closure of a set is smaller than its delta(delta g)star- closure while the delta-interior is generally larger than its delta(delta g)star- interior. In addition, in the same space the delta(delta g)star-continuous functions, absolute-delta(delta g)star- continuous functions and rs -delta(delta g)star - continuous functions are introduced and investigated. Characterization and properties of these functions are also determined.

 

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References

Baculta, J.J., Regular Generalized Star β-sets in Generalized, Bigeneralized and Generalized Fuzzy Topological Spaces Ph. D. Thesis. MSU-Iligan Institute of Technology, Iligan City. (2015)

Dontchev, J. I. Arokiarani, I. and Balanchandran, K., On Generalised δ-Closed Sets and Almost Weakly Hausdorff Spaces., Topology Atlas, (1997).

Dontchev, J. and Ganster. M., On δ-Generalised Closed Sets and T ¾ Spaces, Mem. Fac. Sci. Kochi. Univ. Math. 17 (1996), 5-31.

Dontchev, J. and Noiri, T., Quasi-normal Spaces and πg-Closed Sets. Acta Math. Hungar 89 (3)(2000):211-219.

Dugunji, J., Topology. New Delhi Prentice Hall of India Private Ltd., (1975).

Elvina, M.L., (gs)*-Closed Sets in Topological Spaces. International Journal of Mathematics Trends and Technology, (7)(2014), 83-93.

Gnanambal, Y., On Generalized Pre-regular Sets in Topological Spaces., Ind. J.Pure.Appl.Math 28(3)(1997):351-360.

Jafari, S., Noiri, T., Rajesh, N. and Thivagar, M.L., Another Generalisation of Closed Sets., Kochi.J. Math(3)(2008), 25-38.

Janaki, C., Studies on g-closed Sets in Topological., Ph. D. Thesis Bharathiar University Coimbatore, India (1999).

Levine, N., Semi-open Sets and Semi-continuity in Topological spaces., Amer. Math. Monthly., 70(1963), 36-41.

Levine, N. Generalized Closed sets in Topology., Rend. Circ. Math. Palermo, 19(1970), 89-96.

Maki, H., Devi, R. and Balanchandran, K., Associated Topologies of generalized-closed Sets and α-closed sets and α-generalized closed sets., Mem. Fac. Sci. Kochi Univ. (Math)15(1994), 51-63.

Maki, H., Umehara, J. and Noiri, T., Every Topological Space is Pre-T1/2., Mem.Fac.Sci. Kochi Univ Ser. Alath 17(1996), 33-42.

Meena, K. and Sivakamasundari, K., δ(δg)*-Closed Set in Topological Spaces. Vol.3(7)(2014), 14749-14753.

Palaniappan, N. and Rao K.C., Regular Generalized Closed Sets., Kyungpook Math. J 33(1993), 211-219.

Pushpalatha, A. and Anitha, K., Definition Bank in General Topology and the Properties g*s-Closed Sets in Topological Spaces, Int.J. Contemp.Math Sciences, (6)(2011), 917-929.

Sarsak, M.S. and Rajesh, N., Generalized Semi-pre-Closed Sets. International Mathematical Forum., 5(12)(2010):573-578.

Shylac I.M.T., and Thangavelu, P., On Regular Pre-semi Closed Sets in Topological Spaces.,KBM journal of Mathematical Sciences and Computer Applications, (2010)1(1), 9-17.

Sudha, R. and Sivakamasundari, K., δg*-Closed Sets in Topological Spaces., International Journal of Mathematical Archive, (2012)3(3), 1222-1230.

Thivagar, M.L., Meeradevi, B. and Hatir, E., δg ̂-Closed Sets in Topological Spaces., Gen Math.Notes, (2)(2010), 17-25.

Thivagar, M.L., Meeradevi, B. and Hatir, E., δ-Closed Sets and δg-Closed Sets called δg ̂-Closed Sets ., Gen Math.Notes, Vol.1, No.2, (2010), 17-25.

Vadivel, A. and Vairamanickam, K., rgα-Closed Sets and rgα-Open Sets in Topological Spaces., Int.J.Math Analysis (2010) 3(37);1803-1819.

Veerakumar, M.K.R.S., g ̂-Closed Sets in Topological Spaces., Bull. Allah.Math.soc., (18)(2003), 99-112.

Velicko, N.V., H-Closed Topological Spaces, Amer., Math Soc. Transl., 78(1968), 103-118.

Published
2019-04-19