Full Paper View Go Back

On (gg)*- Closed Sets in Topological Spaces

I. Christal Bai1 , T.Shyla Isac Mary2

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.4 , pp.395-403, Aug-2018


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.395403


Online published on Aug 31, 2018


Copyright © I. Christal Bai, T.Shyla Isac Mary . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library


XML View     PDF Download

How to Cite this Paper

  • IEEE Citation
  • MLA Citation
  • APA Citation
  • BibTex Citation
  • RIS Citation

IEEE Style Citation: I. Christal Bai, T.Shyla Isac Mary, “On (gg)*- Closed Sets in Topological Spaces,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.395-403, 2018.

MLA Style Citation: I. Christal Bai, T.Shyla Isac Mary "On (gg)*- Closed Sets in Topological Spaces." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.4 (2018): 395-403.

APA Style Citation: I. Christal Bai, T.Shyla Isac Mary, (2018). On (gg)*- Closed Sets in Topological Spaces. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(4), 395-403.

BibTex Style Citation:
@article{Bai_2018,
author = {I. Christal Bai, T.Shyla Isac Mary},
title = {On (gg)*- Closed Sets in Topological Spaces},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {8 2018},
volume = {5},
Issue = {4},
month = {8},
year = {2018},
issn = {2347-2693},
pages = {395-403},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=755},
doi = {https://doi.org/10.26438/ijcse/v5i4.395403}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i4.395403}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=755
TI - On (gg)*- Closed Sets in Topological Spaces
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - I. Christal Bai, T.Shyla Isac Mary
PY - 2018
DA - 2018/08/31
PB - IJCSE, Indore, INDIA
SP - 395-403
IS - 4
VL - 5
SN - 2347-2693
ER -

1809 Views    616 Downloads    166 Downloads
  
  

Abstract :
In this paper, we introduce a new class of closed sets called generalization of generalized star closed sets (briefly (gg)* - closed) in topological Spaces. A subset A of a topological space (X , τ) is called (gg)* - closed if U contains regular closure of A whenever U contains A and U is gg-open in (X , τ). We studied the relation of this set with some of the other closed and generalized closed sets and some of the characteristics, of (gg)*- closed sets have been investigated and studied.

Key-Words / Index Term :
(gg)* - closed set, gg - open, regular closure

References :
[1] N .Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 2 , 89- 96, 1970.
[2] D. E. Cameron, Properties of s-closed spaces proc, Amer. Math. Soc., 72, 581-586 ,1978.
[3] M. Stone, Application of the theory of Boolean rings to general topology, Trans. Amer. MathSoci, 412, 374-481, 1937.
[4] Basavaraj M Ittanagi and Govardhana Reddy H G, On gg-Closed Sets in Topological Spaces, International Journal of Mathematical Archive-8(8), 126-133, 2017.
[5] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70, 36-41, 1963.
[6] A.S. Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, On pre-continious and weak pre- continious mappings, Proc. Math and Phys. Soc. Egypt ,53, 47-53,1982.
[7] D. Andrijevic, Semi-preopen sets, Mat. Vesnik 38 ,24-32, 1986.
[8] O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15, 961-970, 1965.
[9] T.Indira and K. Rekha, Applications of *b-open sets and **b-open sets in Topological Spaces, Annals of pure and Applied Mathematics, 1, 44-56, 2012 .
[10] J. Dontchev, On generalizing semi-pre-open sets, Mem. Fac. Sci. Kochi Univ. ser. A. Math.,
16, 35-48 ,1995.
[11] H. Maki, J. Umehara and T. Noiri, Generalized preclosed sets, Mem. Fac. Sci. Kochi Univ.
Ser. A. Math, 17, 33-42, 1996.
[12] S.P. Arya and T.M.Nour, Characterizations of s-normal spaces, Indian J. Pure. Appl. Math.,21 (8), 717-719 ,1990.
[13] H. Maki, R. Devi and K. Balachandran, Associated topologies of generalized α -closed sets and α -generalized closed sets, Mem. Fac. sci. Kochi. Univ. Ser. A. Math.,15, 51-63, 1994.
[14 ] N. Palaniappan and K.C. Rao, Regular generalized closed sets, Kyungpook Math.J.,33, 211-219, 1993.
[15] Y. Gnanambal, On generalized pre regular closed sets in topological spaces, Indian J. Pure. Appl. Math., 28 (3),351-360,1997.
[16] G.B Navalagi and Chandrashekarappa, On gspr closed sets in topological spaces, Vol.2,Nos 1-2, pp.35-44, 2010.
[17] M.K.R.S.Veerakumar, g*-preclosed sets, Acta Ciencia India, Vol.XXVIII M, 1, 51- 60, 2002.
[18] A. Pushpalatha, Studies on gereralizations of mappings in topological space, ph.D. Thesis, Bharathiar University Coimbatore, 2000.
[19] Ahmed A.El.Mabhouh and Hanady A.Al-Faiuomy, tgr-Closed Sets and t*gr-Closed Sets. International Mathematical Forum, Vol. 10, No. 5, 211 – 220, 2015.
[20] S.S. Benchalli and R.S.Walli, On RW-closed sets in topological spaces, Bull. Malaysian.Math. Sci.Soc., (2)30(2), 99-110, 2007.
[21] A.Vadivel and K.Vairamanickam, rgα-closed sets and rgα -open sets in topological Spaces, Int. Journal of Math. Analysis, 3 (37), 1803-1819, 2009
[22] H. Maki, R. Devi and K. Balachandran, generalized α -closed sets in topology, Bull. Fukuoka Univ. Ed. Part (2), 42, 13-21, 1993.
[23] P. Bhattacharya and B.K. Lahiri , Semi-generalized closed sets in topological spaces,
Indian J. Math, 29, 376-382, 1987.
[24] C. Janaki and Renu Thomas, On R* closed sets in topological spaces, International
Journal of Mathematical Archive, 3(8), 3067-3074 , 2012.
[25] Basavaraj M Ittanagi and Raghavendra. K, On R#-Closed Sets in Topological Spaces, International Journal of Mathematical Archive-8(8), 134-141, 2017.
[26] C. Dhanapakyam, k. Indirani, On βg* closed sets in topological Spaces, International journal of Applied Research ,2(4),388-391, 2016.
[27] D. Savithiri and C Janaki , On Regular^Generalized closed sets in topological spaces International Journal of Mathematical Archive, 4(4), 162-169, 2013.
[28] M. Pauline Mary Helen, Veronica Vijayan, Ponnuthai Selvarani, g** closed sets in Topological Spaces, IJMA, 3(5), 1-15, 2012.
[29] P. Sundaram and M. Sheik John, On w-closed sets in topology, Acta, Ciencia Indica, 4, 389-392, 2000.
[30] S. Bhattacharya, On Generalized Regular Closed Sets, Int. J.Contemp. Math. Sciences, 6 , 145-152, 2011.
[31] K. Indirani, P.Sathishmohan and V. Rajendran, On gr*-Closed sets in a Topological Spaces, International journal of Mathematics trends and Technology, Vol, feb 2014.

Authorization Required

 

You do not have rights to view the full text article.
Please contact administration for subscription to Journal or individual article.
Mail us at  support@isroset.org or view contact page for more details.

Go to Navigation