New notions in ideal topological space
DOI:
https://doi.org/10.5269/bspm.v38i5.37053Palavras-chave:
I∗∗α g -closed sets, I∗∗α g -open sets, I∗∗α g -locally closed sets, I∗∗α g -submaximal spacesResumo
In this paper, we apply the notion of I∗∗α g -closed sets to present and study a new class of locally closed sets called I∗∗α g -locally closed sets in ideal topological spaces along with their several characterizations and mutual relationships between the new notion and other locally closed sets. Further we introduce I∗∗α g-submaximal space and some properties of such notion are investigated.Referências
1. Acikgoz.A, Yuksel.S and Noiri.T, On α-I-preirresolute functions and β-I-preirresolute functions, Bull. Malays. Math. Sci. Soc. 2,28(1),1-8,(2005).
2. Balachandran.K, Sundaram.P and Maki.H, Generalized locally closed sets and GLCContinuous functions, Indian J. Pure and Appl. Math.,27(3),235-244,(1996).
3. Bhavani.K, Sivaraj.D, Ig-Submaximal space, Bol. Soc.Paran.Mat.Volume 33(1),105- 110,(2015).
4. Bourbaki.N General topology, part I. Addison Wesley Reading Mass,(1996).
5. Dontchev.J, Idealization of Ganster Reilly Decomposition Theorems, Math.GN/990- 1017,(5),Jan.1999.
6. Dontchev.J, Ganster.M, Noiri.T, Unified operation approach of generalized closed sets via topological ideal, Math.Japanica 49,395-401,(1999) .
7. Erdal Ekici and Takashi Noiri, Properties of I-Submaximal ideal topological spaces, Faculty of sciences and mathematics, Filomat 24:4,87-94,(2010).
8. Erdal Ekici and Takashi Noiri, Connectedness in ideal topological spaces, Novi Sad J.Math.Vol.38,No.2,65-70,(2008) .
9. E. Hewitt, A problem of set-theoretic topology, Duke Math.J.,10,309-333,(1943).
10. Jankovic.D, Hamlett.T.R, New topologies from old via ideals, Amer.Math.Monthly 97,295- 310,(1990).
11. Jeong Gi Kang and Chang Su Gim, On P-I open sets, Honam Mathematical J.31, No.3,pp.293-314,(2009).
12. Krishnan Balachandran, Palaniappan Sundaram and Haruo Maki, Generalized locally closed sets and GLC-continuous functions,Indian J.Pure Appl. Math. 27(3). 235-244(1996).
13. Kuratowski.K, Topology,Vol.I.Academic press, New York, (1966).
14. Levine.N, Generalized closed sets in topology, Rend. Circ.Mat.Palermo 19,89-96,(1970).
15. Rajamani.M, Indhumathi.V and Krishnaprakash.S, Some stronger local function via ideals,J.Adv.Res.Pure Math.,2,48-52,(2010).
16. Rajamani.M, Indhumathi.V and Krishnaprakash.S, On I ∗α g -closed sets and I ∗α g -continuity, Jordan Journal of Mathematics and Statistics,5(3),201-208,(2012).
17. Navaneethakrishnan.M and Sivaraj.D, Generalized locally closed sets in ideal topological spaces, Bull. Allahabad Math.Soc,Vol.24, Part1,13-19,(2009).
18. Nasef A.A, Radwan A.E, Esmaeel.R.B, Some properties of α-open sets with respect to an ideal, International Journal of Pure and Applied Mathematics Volume 102 No.4,613- 630,(2015).
19. Njastad.O, On some classes of nearly open sets, Pascific J. Math.,15,961-970,(1965).
20. Santhini.C, Suganya.M, New form of generalized closed sets via ideal topology, Proceedings of International Conference on Recent Trends in Applied mathematics,S.R.N.M College,Sattur,(2017).
2. Balachandran.K, Sundaram.P and Maki.H, Generalized locally closed sets and GLCContinuous functions, Indian J. Pure and Appl. Math.,27(3),235-244,(1996).
3. Bhavani.K, Sivaraj.D, Ig-Submaximal space, Bol. Soc.Paran.Mat.Volume 33(1),105- 110,(2015).
4. Bourbaki.N General topology, part I. Addison Wesley Reading Mass,(1996).
5. Dontchev.J, Idealization of Ganster Reilly Decomposition Theorems, Math.GN/990- 1017,(5),Jan.1999.
6. Dontchev.J, Ganster.M, Noiri.T, Unified operation approach of generalized closed sets via topological ideal, Math.Japanica 49,395-401,(1999) .
7. Erdal Ekici and Takashi Noiri, Properties of I-Submaximal ideal topological spaces, Faculty of sciences and mathematics, Filomat 24:4,87-94,(2010).
8. Erdal Ekici and Takashi Noiri, Connectedness in ideal topological spaces, Novi Sad J.Math.Vol.38,No.2,65-70,(2008) .
9. E. Hewitt, A problem of set-theoretic topology, Duke Math.J.,10,309-333,(1943).
10. Jankovic.D, Hamlett.T.R, New topologies from old via ideals, Amer.Math.Monthly 97,295- 310,(1990).
11. Jeong Gi Kang and Chang Su Gim, On P-I open sets, Honam Mathematical J.31, No.3,pp.293-314,(2009).
12. Krishnan Balachandran, Palaniappan Sundaram and Haruo Maki, Generalized locally closed sets and GLC-continuous functions,Indian J.Pure Appl. Math. 27(3). 235-244(1996).
13. Kuratowski.K, Topology,Vol.I.Academic press, New York, (1966).
14. Levine.N, Generalized closed sets in topology, Rend. Circ.Mat.Palermo 19,89-96,(1970).
15. Rajamani.M, Indhumathi.V and Krishnaprakash.S, Some stronger local function via ideals,J.Adv.Res.Pure Math.,2,48-52,(2010).
16. Rajamani.M, Indhumathi.V and Krishnaprakash.S, On I ∗α g -closed sets and I ∗α g -continuity, Jordan Journal of Mathematics and Statistics,5(3),201-208,(2012).
17. Navaneethakrishnan.M and Sivaraj.D, Generalized locally closed sets in ideal topological spaces, Bull. Allahabad Math.Soc,Vol.24, Part1,13-19,(2009).
18. Nasef A.A, Radwan A.E, Esmaeel.R.B, Some properties of α-open sets with respect to an ideal, International Journal of Pure and Applied Mathematics Volume 102 No.4,613- 630,(2015).
19. Njastad.O, On some classes of nearly open sets, Pascific J. Math.,15,961-970,(1965).
20. Santhini.C, Suganya.M, New form of generalized closed sets via ideal topology, Proceedings of International Conference on Recent Trends in Applied mathematics,S.R.N.M College,Sattur,(2017).
Downloads
Publicado
2019-03-31
Edição
Seção
Artigos
Licença
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
