On Generalization of Generalized star generalized closed sets in Topological Spaces
Abstract
In this paper we introduce a new class of closed sets called generalization of generalized star generalized closed sets (briefly - closed) in topological spaces. And also we scrutinized some of their characterization and its relationship along other closed sets.
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References
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Ahmad Al-Omari and Mohd Salmi Md Noorani, Regular Generalized w-Closed Sets, International Journal of Mathematics and Mathematical Sciences, Volume 2007, Article ID 16292.
Basavaraj M. Ittanagi and Govardhana Reddy H.G/ On gg-Closed Sets in Topological Spaces / IJMA-8(8), August 2017.
Basavaraj M. Ittanagi and Raghavendra K / On R#-Closed Sets in Topological Spaces/ IJMA-8(8), August 2017.
Benchalli S.S & R.S Wali, On RW - Closed Sets in Topological Spaces, Bull. Malay. Math. Sci. Soc. (2) 30(2) (2007), 99-110.
Benchalli S.S and J.B Toranagatti, Delta Generalized Pre-Closed Sets in Topological Spaces; IJCMS: Vol. 11, 2016, no. 6, 281-292.
Bhattacharya S(Halder), On Generalized Regular Closed Sets, Int.J. Contemp. Math,Sciences, Vol.6, 2011, no.3, 145 – 152.
Cameron D.E, Properties of semi closed Spaces Proc, Amer – Math – Soc, 72, 581-586, 1978.
Christal BaiI, T.Shyla Isac Mary/On (gg)* - Closed Sets in Topological Spaces / IJSR in MSS, S(4)(2018), 395-403.
Dhana Lekshmi D, T. Shyla Isac Mary, w*s - Closed Sets in Topological Spaces, Journal of Harbin Engineering University, ISSN:1006-7043, Vol 44, No. 8 August 2023.
DillyRani C, Generalized Pre-Closed Set in Topological Spaces, IJRES, www.ijres.org Volume 09 Issue 12\2021\PP. 19-23.
Dontchev J and T.Noiri, Quasi – Normal Spaces and πg - Closed Sets, Acta Math. Hungar 89(3) (2000), 211-219
Govindappa Navalagi, Chandrashekarappa A.S and S.V. Gurushantanavar, On GSPR – Closed Sets in Topological Spaces, IJMCA, Vol. 2, No. 1-2, January – December 2010, PP.51-58.
Govindappa Navalagiand Kantappa. M. Bhavikatti, Beta Weakly Generalized Closed Sets in Topology, JCMS, Vol. 9(5), May2018, www.compmath-journal.org, 435-446.
Indirani K, P. Satishmohan and V. Rajendran, On gr* - Closed Sets in Topological Spaces, International Journal of Mathematics Trends and Technology – volume 6 - February 2014.
Jayakumar et al P, On Generalized gp* - Closed Set in Topological Spaces / Int.Journal of Math. Analysis, Vol. 7, 2013, no. 33, 1635-1645.
Jilling Cao, Maximilian Ganster, Ivan Reilly, On Generalized Closed Sets, J.Cao et al./Topology and its applications 123 (2002) 37 – 46.
Maki H, R. Devi and K. Balachandran, Generalized Alpha Closed Sets in Topology, Bull. Fukuoka Univ. Ed. Part (2),42, (1993) 13-21.
Manonmani A, S. Jayalakshmi, On Regular Beta (rβ) - Closed Sets in Topological Spaces, Research Gate Impact factor (2018): 0.28/ SJIF (2018): 7.426.
Meena K & V. P Anuja On Alpha ^ Generalized Closed Sets in Topological Spaces / Journal of Xian Shiyou University, Natural since edition, ISSN:1673-064X.
Mishra S, V. Joshi, N. Bhardwaj, On Generalized Pre Regular Weakly(gprw) – Closed Sets in Topological Spaces, IMF, Vol. 7, 2012, No. 40, 1981-1992.
Mukundhan C, N. Nagaveni, A weaker form of a Generalized Closed Set, Int. J. Contemp. Maths. Sciences, Vol. 6, 2011, No. 20, 949-961.
Meena kumari N & T. Indira, r*g* - Closed Sets in Topological Spaces, www.researchmathsci.org, APAM: Vol. 6, No. 2, 2014, 125-132.
Nitin Bhardwaj, Harpreet Kaur, B. P. Garg, On Regular β - Generalized Closed Sets in Topological Spaces / GJPAM.ISSN 0973-1768 Volume 11, Number 2 (2015), pp. 875-886.
Norman Levine, Generalized Closed Sets in Topology, Rend Cir.Mat.Palamo 2(1970), 89 – 96.
Palaniappan N and K. Chandra sekhar Rao / Regular Generalized Closed Sets/ Kyungpook Math.J(1993) 33, 211 – 219.
Parimelazhagan R and V. Subramonia Pillai, Strongly g*- Closed Sets in Topological Spaces, Int.Journal of Math. Analysis, Vol.6, 2012, no .30, 1481 – 1489.
Pauline Mary Helen M, (gsp)* - Closed Sets in Topological Spaces / International Journal of Mathematics trends and technology – volume 6 – February 2014.
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Ponmalar P, Between Strongly g - Closed Sets and Strongly g** - Closed Sets in Topological Spaces 2019 JET 1R March 2019, Volume 6, Issue 3, www.jetir.org (ISSN – 2349 – 5162).
Savithiri D and Janaki C, On Regular ^ Generalized Closed Sets in Topological Spaces, International Journal of Mathematics Archive – 4(4), 2013, 162-169.
Sekar C and Rajakumari, On Alpha Generalized Star Pre-Closed Sets in Topological Spaces, IJMER.
Sekar S, G. Kumar, On gαr - Closed Sets in Topological Spaces, IJPAM, Volume 108 No. 4 2016, 791-800.
Sekar S and S. Loganayagi, On Generalized b Star - Closed Set in Topological Spaces, Malaya J. Mat. 5(2)(2017) 401-406.
Shaini Melina, M Trinita Pricilla, On (gαr)** - Closed Sets in Topological Spaces IJCRT /Volume 10, Issue 3 march 2022/ISSN:2320-2882.
Shyla Isac Mary T & G. Abirami α(gg)* - Closed Sets in Topological Spaces / IJMTT, 2022, 68(3), 5-10.
Sreeja D and S. Sasikala / Generalized Star Semi Regular Closed Sets in Topological Spaces / Malaya J.Mat S(1)(2015)42-56.
Velicko N V, H-Closed Topological Spaces, Amer.math.soc. Transl.78(1968), 103-116.
Vidhya D and R. Parimelazhagan, g*b - Closed Sets in Topological Spaces, Int. J. Contemp. Math. Sciences, Vol. 7(2022), no. 27, 1305-1312.
D. Andrijevi´c. On b-open sets. Matematicki Vesnik, 48:59–64, 1996.
C. Boonpok. (Λ, sp)-closed sets and related topics in topological spaces. WSEAS Transactions on Mathematics, 19:321–322, 2020.
C. L. Chang. Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 24:182–190, 1968.
G. Senel and N. Cagman. Soft closed sets on soft bitopological spaces. Journal of New Results in Science, 5:57–66, 2014.
G. Senel and N. Cagman. Soft topological subspaces. Annals of Fuzzy Mathematics and Informatics, 10(4):525–535, 2015.
W. Dunham and N. Levine. Further results on generalized closed sets. Kyungpook Mathematical Journal, 20:169–175, 1980.
M. E. Abd El-Monsef, S. N. El-Deeb, and R. A. Mahmoud. β-open sets and β continuous mappings. Bulletin of the Faculty of Science. Assiut University., 12:77–90, 1983.
E. F. Lashin, A. M. Kozae, A. A. Abo Khadra, and T. Medhat. Rough set for topological spaces. International Journal of Approximate Reasoning, 40:35–43, 2005.
[N. Levine. Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly, 70:36–41, 1963.
N. Levine. Generalized closed sets in topology. Rendiconti del Circolo Matematico de Palermo (2), 19:89–96, 1970.
A. S. Mashhour, M. E. El-Monsef, and S. N. El-Deeb. On precontinuous and weak precontinuous mappings. Proceedings of the Mathematical and Physical Society of Egypt, 53:47–53, 1982.
O. Njastad. On some classes of nearly open sets. Pasific Journal of Mathematics, 15:961–970, 1965.
T. Noiri and E. Hatir. Λsp-sets and some weak separation axioms. Acta Mathematica Hungarica, 103(3):225–232, 2004.
M. Shabir and M. Naz. On soft topological spaces. Computers and Mathematics with Applications, 61:1786–1799, 2011
Ahmad Al-Omari and Mohd Salmi Md Noorani, Regular Generalized w-Closed Sets, International Journal of Mathematics and Mathematical Sciences, Volume 2007, Article ID 16292.
Basavaraj M. Ittanagi and Govardhana Reddy H.G/ On gg-Closed Sets in Topological Spaces / IJMA-8(8), August 2017.
Basavaraj M. Ittanagi and Raghavendra K / On R#-Closed Sets in Topological Spaces/ IJMA-8(8), August 2017.
Benchalli S.S & R.S Wali, On RW - Closed Sets in Topological Spaces, Bull. Malay. Math. Sci. Soc. (2) 30(2) (2007), 99-110.
Benchalli S.S and J.B Toranagatti, Delta Generalized Pre-Closed Sets in Topological Spaces; IJCMS: Vol. 11, 2016, no. 6, 281-292.
Bhattacharya S(Halder), On Generalized Regular Closed Sets, Int.J. Contemp. Math,Sciences, Vol.6, 2011, no.3, 145 – 152.
Cameron D.E, Properties of semi closed Spaces Proc, Amer – Math – Soc, 72, 581-586, 1978.
Christal BaiI, T.Shyla Isac Mary/On (gg)* - Closed Sets in Topological Spaces / IJSR in MSS, S(4)(2018), 395-403.
Dhana Lekshmi D, T. Shyla Isac Mary, w*s - Closed Sets in Topological Spaces, Journal of Harbin Engineering University, ISSN:1006-7043, Vol 44, No. 8 August 2023.
DillyRani C, Generalized Pre-Closed Set in Topological Spaces, IJRES, www.ijres.org Volume 09 Issue 12\2021\PP. 19-23.
Dontchev J and T.Noiri, Quasi – Normal Spaces and πg - Closed Sets, Acta Math. Hungar 89(3) (2000), 211-219
Govindappa Navalagi, Chandrashekarappa A.S and S.V. Gurushantanavar, On GSPR – Closed Sets in Topological Spaces, IJMCA, Vol. 2, No. 1-2, January – December 2010, PP.51-58.
Govindappa Navalagiand Kantappa. M. Bhavikatti, Beta Weakly Generalized Closed Sets in Topology, JCMS, Vol. 9(5), May2018, www.compmath-journal.org, 435-446.
Indirani K, P. Satishmohan and V. Rajendran, On gr* - Closed Sets in Topological Spaces, International Journal of Mathematics Trends and Technology – volume 6 - February 2014.
Jayakumar et al P, On Generalized gp* - Closed Set in Topological Spaces / Int.Journal of Math. Analysis, Vol. 7, 2013, no. 33, 1635-1645.
Jilling Cao, Maximilian Ganster, Ivan Reilly, On Generalized Closed Sets, J.Cao et al./Topology and its applications 123 (2002) 37 – 46.
Maki H, R. Devi and K. Balachandran, Generalized Alpha Closed Sets in Topology, Bull. Fukuoka Univ. Ed. Part (2),42, (1993) 13-21.
Manonmani A, S. Jayalakshmi, On Regular Beta (rβ) - Closed Sets in Topological Spaces, Research Gate Impact factor (2018): 0.28/ SJIF (2018): 7.426.
Meena K & V. P Anuja On Alpha ^ Generalized Closed Sets in Topological Spaces / Journal of Xian Shiyou University, Natural since edition, ISSN:1673-064X.
Mishra S, V. Joshi, N. Bhardwaj, On Generalized Pre Regular Weakly(gprw) – Closed Sets in Topological Spaces, IMF, Vol. 7, 2012, No. 40, 1981-1992.
Mukundhan C, N. Nagaveni, A weaker form of a Generalized Closed Set, Int. J. Contemp. Maths. Sciences, Vol. 6, 2011, No. 20, 949-961.
Meena kumari N & T. Indira, r*g* - Closed Sets in Topological Spaces, www.researchmathsci.org, APAM: Vol. 6, No. 2, 2014, 125-132.
Nitin Bhardwaj, Harpreet Kaur, B. P. Garg, On Regular β - Generalized Closed Sets in Topological Spaces / GJPAM.ISSN 0973-1768 Volume 11, Number 2 (2015), pp. 875-886.
Norman Levine, Generalized Closed Sets in Topology, Rend Cir.Mat.Palamo 2(1970), 89 – 96.
Palaniappan N and K. Chandra sekhar Rao / Regular Generalized Closed Sets/ Kyungpook Math.J(1993) 33, 211 – 219.
Parimelazhagan R and V. Subramonia Pillai, Strongly g*- Closed Sets in Topological Spaces, Int.Journal of Math. Analysis, Vol.6, 2012, no .30, 1481 – 1489.
Pauline Mary Helen M, (gsp)* - Closed Sets in Topological Spaces / International Journal of Mathematics trends and technology – volume 6 – February 2014.
Paulin Mary Helen M, (g*p)* - Closed Sets In Topological Spaces. International Journal of Mathematics Trends and Technology – Volume 6 – February 2014 ISSN: 2231-5373 http://www.ijmttjournal.org Page 87.
Ponmalar P, Between Strongly g - Closed Sets and Strongly g** - Closed Sets in Topological Spaces 2019 JET 1R March 2019, Volume 6, Issue 3, www.jetir.org (ISSN – 2349 – 5162).
Savithiri D and Janaki C, On Regular ^ Generalized Closed Sets in Topological Spaces, International Journal of Mathematics Archive – 4(4), 2013, 162-169.
Sekar C and Rajakumari, On Alpha Generalized Star Pre-Closed Sets in Topological Spaces, IJMER.
Sekar S, G. Kumar, On gαr - Closed Sets in Topological Spaces, IJPAM, Volume 108 No. 4 2016, 791-800.
Sekar S and S. Loganayagi, On Generalized b Star - Closed Set in Topological Spaces, Malaya J. Mat. 5(2)(2017) 401-406.
Shaini Melina, M Trinita Pricilla, On (gαr)** - Closed Sets in Topological Spaces IJCRT /Volume 10, Issue 3 march 2022/ISSN:2320-2882.
Shyla Isac Mary T & G. Abirami α(gg)* - Closed Sets in Topological Spaces / IJMTT, 2022, 68(3), 5-10.
Sreeja D and S. Sasikala / Generalized Star Semi Regular Closed Sets in Topological Spaces / Malaya J.Mat S(1)(2015)42-56.
Velicko N V, H-Closed Topological Spaces, Amer.math.soc. Transl.78(1968), 103-116.
Vidhya D and R. Parimelazhagan, g*b - Closed Sets in Topological Spaces, Int. J. Contemp. Math. Sciences, Vol. 7(2022), no. 27, 1305-1312.
D. Andrijevi´c. On b-open sets. Matematicki Vesnik, 48:59–64, 1996.
C. Boonpok. (Λ, sp)-closed sets and related topics in topological spaces. WSEAS Transactions on Mathematics, 19:321–322, 2020.
C. L. Chang. Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 24:182–190, 1968.
G. Senel and N. Cagman. Soft closed sets on soft bitopological spaces. Journal of New Results in Science, 5:57–66, 2014.
G. Senel and N. Cagman. Soft topological subspaces. Annals of Fuzzy Mathematics and Informatics, 10(4):525–535, 2015.
W. Dunham and N. Levine. Further results on generalized closed sets. Kyungpook Mathematical Journal, 20:169–175, 1980.
M. E. Abd El-Monsef, S. N. El-Deeb, and R. A. Mahmoud. β-open sets and β continuous mappings. Bulletin of the Faculty of Science. Assiut University., 12:77–90, 1983.
E. F. Lashin, A. M. Kozae, A. A. Abo Khadra, and T. Medhat. Rough set for topological spaces. International Journal of Approximate Reasoning, 40:35–43, 2005.
[N. Levine. Semi-open sets and semi-continuity in topological spaces. The American Mathematical Monthly, 70:36–41, 1963.
N. Levine. Generalized closed sets in topology. Rendiconti del Circolo Matematico de Palermo (2), 19:89–96, 1970.
A. S. Mashhour, M. E. El-Monsef, and S. N. El-Deeb. On precontinuous and weak precontinuous mappings. Proceedings of the Mathematical and Physical Society of Egypt, 53:47–53, 1982.
O. Njastad. On some classes of nearly open sets. Pasific Journal of Mathematics, 15:961–970, 1965.
T. Noiri and E. Hatir. Λsp-sets and some weak separation axioms. Acta Mathematica Hungarica, 103(3):225–232, 2004.
M. Shabir and M. Naz. On soft topological spaces. Computers and Mathematics with Applications, 61:1786–1799, 2011
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2026-03-26
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