δ(δg)* - Sets and Functions in Topological Spaces
DOI:
https://doi.org/10.53555/ms.v5i4.833Keywords:
Keywords: δ(δg)* - set, δ(δg)* - closure, δ(δg)*-continuous functions, absolute-δ(δg)* - continuous functions, rs - δ(δg)* - continuous functionsAbstract
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.
Downloads
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.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 International Journal For Research In Mathematics And Statistics (ISSN: 2208-2662)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
In consideration of the journal, Green Publication taking action in reviewing and editing our manuscript, the authors undersigned hereby transfer, assign, or otherwise convey all copyright ownership to the Editorial Office of the Green Publication in the event that such work is published in the journal. Such conveyance covers any product that may derive from the published journal, whether print or electronic. Green Publication shall have the right to register copyright to the Article in its name as claimant, whether separately
or as part of the journal issue or other medium in which the Article is included.
By signing this Agreement, the author(s), and in the case of a Work Made For Hire, the employer, jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties, and that the Article has not been published elsewhere, and is not being considered for publication elsewhere in any form, except as provided herein. Each author’s signature should appear below. The signing author(s) (and, in