Research Article
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On Strong Pre*-I-Open Sets in Ideal Topological Spaces

Year 2019, Issue: 28, 44 - 52, 07.05.2019

Abstract

The aim of the present paper is to introduce the class of strong pre*-I-open sets which is strictly placed between the class of all pre-I-open and the class of all pre*-I-open subsets of X. Relationships with some other types of sets were given. Furthermore, by using the new notion, we defined the strong pre*-I-Interior and strong pre*I-closure operators and established their various properties.

References

  • K. Kuratowski, Topology, Vol. I, Academic Press, NewYork 1966.
  • D. Jankovi´c, T.R.Hamlett, New topologies from old via ideals, Amer. Math. Monthly 97 (1990) 295-310.
  • M. E. Abd El-monsef, E. F. Lashien, A. A. Nasef, On I-open sets and I-continuous functions, Kyungpook Math 32 (1992) 21-30.
  • J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, arxiv: math GN/9901017v1(1999).
  • E. Hatir, T. Noiri, On decompositions of continuity via idealization, Acta Math. Hungar 96(4) (2002) 341-349.
  • E. Ekici, On ACI -sets, BCI -sets, \beta^*I -open sets and decompositions of continuity in ideal topological spaces, Creat. Math. Inform 20(1) (2011) 47-54.
  • A. Keskin, S. Yuksel, T. Noiri, Decompositions of I-continuity and continuity, Commun.Fac. Sci. Univ. Ank. Ser. A1 53(2) (2004) 67-75.
  • A.S. Mashhour, M. E. Abd El-monsef, S. N. El-deep, On precontinuous and weak precontinuous mappings, Proc. Math.Phys soc. Egypt 53 (1982), 47-53.
  • E. Ekici, On A^*_I-sets, C_I-sets, C^*_I-sets and decompositions of continuity in ideal topological spaces, Anal. Al. I. Cuza Univ. Math 2013, DOI: 10.2478/v10157-012-0030-y.
  • R. M. Aqeel, A. A. Bin Kuddah, On strong semi*-I-open sets in ideal topological spaces, Aden University Journal of Natural and Applied Sciences (Accepted).
  • E. Hatir, A. Keskin, T. Noiri, On a new decomposition of continuity via idealization, JP J. Geometry Topology 3(1) (2003) 53-64.
  • M. E. Abd El-Monsef, S. N. El-Deeb, R. A. Mahmoud, \beta -open sets and \beta- continuous mappings , Bull. Fac. Sci. Assiut Univ 12 (1983) 77-90.
  • E. Hatir and S. Jafari, On weakly semi-I-open sets and another decomposition continuity via ideals, Sarajevo J. Math 2(14) (2006) 107-114.
  • E. Hatir, A. Keskin, T. Noiri, A note on strong \beta-I-open sets and strongly \beta-I-continuous functions, Acta Math. Hungar 108(1-2) (2005) 87-94.
  • E. Hayashi, Topologies defined by local properties, Math. Ann 156 (1964) 205-215.
  • J.Dontchev, M. Ganster, D. Rose, Ideal resolvability, Topology Appl 93 (1) (1999), 1-16.
  • V. Renukadevi, D. Sivaraj, A decomposition of continuity via ideals, Acta. Math.Hungar 118 (1-2) (2008) 53-59.
  • E. Ekici, On pre-I-open sets, semi-I-open sets and b-I-open sets in ideal topological spaces, Acta Univ. Apulensis 30 (2012) 293-303.
  • E. G. Yang, A round decompositions of continuity via idealization ,Questions Answers General Topology 26 (2008) 131-138.
  • E. Ekici, T .Noiri, \emph{*-extremally disconnected ideal topological spaces}, Acta Math.Hungar 122 (2009) 81-90.
Year 2019, Issue: 28, 44 - 52, 07.05.2019

Abstract

References

  • K. Kuratowski, Topology, Vol. I, Academic Press, NewYork 1966.
  • D. Jankovi´c, T.R.Hamlett, New topologies from old via ideals, Amer. Math. Monthly 97 (1990) 295-310.
  • M. E. Abd El-monsef, E. F. Lashien, A. A. Nasef, On I-open sets and I-continuous functions, Kyungpook Math 32 (1992) 21-30.
  • J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, arxiv: math GN/9901017v1(1999).
  • E. Hatir, T. Noiri, On decompositions of continuity via idealization, Acta Math. Hungar 96(4) (2002) 341-349.
  • E. Ekici, On ACI -sets, BCI -sets, \beta^*I -open sets and decompositions of continuity in ideal topological spaces, Creat. Math. Inform 20(1) (2011) 47-54.
  • A. Keskin, S. Yuksel, T. Noiri, Decompositions of I-continuity and continuity, Commun.Fac. Sci. Univ. Ank. Ser. A1 53(2) (2004) 67-75.
  • A.S. Mashhour, M. E. Abd El-monsef, S. N. El-deep, On precontinuous and weak precontinuous mappings, Proc. Math.Phys soc. Egypt 53 (1982), 47-53.
  • E. Ekici, On A^*_I-sets, C_I-sets, C^*_I-sets and decompositions of continuity in ideal topological spaces, Anal. Al. I. Cuza Univ. Math 2013, DOI: 10.2478/v10157-012-0030-y.
  • R. M. Aqeel, A. A. Bin Kuddah, On strong semi*-I-open sets in ideal topological spaces, Aden University Journal of Natural and Applied Sciences (Accepted).
  • E. Hatir, A. Keskin, T. Noiri, On a new decomposition of continuity via idealization, JP J. Geometry Topology 3(1) (2003) 53-64.
  • M. E. Abd El-Monsef, S. N. El-Deeb, R. A. Mahmoud, \beta -open sets and \beta- continuous mappings , Bull. Fac. Sci. Assiut Univ 12 (1983) 77-90.
  • E. Hatir and S. Jafari, On weakly semi-I-open sets and another decomposition continuity via ideals, Sarajevo J. Math 2(14) (2006) 107-114.
  • E. Hatir, A. Keskin, T. Noiri, A note on strong \beta-I-open sets and strongly \beta-I-continuous functions, Acta Math. Hungar 108(1-2) (2005) 87-94.
  • E. Hayashi, Topologies defined by local properties, Math. Ann 156 (1964) 205-215.
  • J.Dontchev, M. Ganster, D. Rose, Ideal resolvability, Topology Appl 93 (1) (1999), 1-16.
  • V. Renukadevi, D. Sivaraj, A decomposition of continuity via ideals, Acta. Math.Hungar 118 (1-2) (2008) 53-59.
  • E. Ekici, On pre-I-open sets, semi-I-open sets and b-I-open sets in ideal topological spaces, Acta Univ. Apulensis 30 (2012) 293-303.
  • E. G. Yang, A round decompositions of continuity via idealization ,Questions Answers General Topology 26 (2008) 131-138.
  • E. Ekici, T .Noiri, \emph{*-extremally disconnected ideal topological spaces}, Acta Math.Hungar 122 (2009) 81-90.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Radhwan Mohammed Aqeel

Ahlam Abdullah Bin Kuddah This is me

Publication Date May 7, 2019
Submission Date November 30, 2018
Published in Issue Year 2019 Issue: 28

Cite

APA Aqeel, R. M., & Bin Kuddah, A. A. (2019). On Strong Pre*-I-Open Sets in Ideal Topological Spaces. Journal of New Theory(28), 44-52.
AMA Aqeel RM, Bin Kuddah AA. On Strong Pre*-I-Open Sets in Ideal Topological Spaces. JNT. May 2019;(28):44-52.
Chicago Aqeel, Radhwan Mohammed, and Ahlam Abdullah Bin Kuddah. “On Strong Pre*-I-Open Sets in Ideal Topological Spaces”. Journal of New Theory, no. 28 (May 2019): 44-52.
EndNote Aqeel RM, Bin Kuddah AA (May 1, 2019) On Strong Pre*-I-Open Sets in Ideal Topological Spaces. Journal of New Theory 28 44–52.
IEEE R. M. Aqeel and A. A. Bin Kuddah, “On Strong Pre*-I-Open Sets in Ideal Topological Spaces”, JNT, no. 28, pp. 44–52, May 2019.
ISNAD Aqeel, Radhwan Mohammed - Bin Kuddah, Ahlam Abdullah. “On Strong Pre*-I-Open Sets in Ideal Topological Spaces”. Journal of New Theory 28 (May 2019), 44-52.
JAMA Aqeel RM, Bin Kuddah AA. On Strong Pre*-I-Open Sets in Ideal Topological Spaces. JNT. 2019;:44–52.
MLA Aqeel, Radhwan Mohammed and Ahlam Abdullah Bin Kuddah. “On Strong Pre*-I-Open Sets in Ideal Topological Spaces”. Journal of New Theory, no. 28, 2019, pp. 44-52.
Vancouver Aqeel RM, Bin Kuddah AA. On Strong Pre*-I-Open Sets in Ideal Topological Spaces. JNT. 2019(28):44-52.


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