Semi generalization of δI*-closed sets in ideal topological space

Authors

  • K Palani Associate Professor and Head, PG & Research Department of Mathematics, A.P.C Mahalaxmi College for Women, Thoothukudi-2. Tamilnadu
  • M Karthigai Jothi Research Scholar, Reg. No: 21212012092005, PG & Research Department of Mathematics, A.P.C Mahalaxmi College for Women, Thoothukudi-2. ManonmaniamSundaranar University, Abishekapatti, Tirunelveli -12. Tamilnadu

DOI:

https://doi.org/10.23755/rm.v44i0.925

Keywords:

ideal topological space, I*-closed sets, gsI*-closed sets

Abstract

In this paper we introduce the notion of semi generalized dI*-closed sets or gsdI*-closed sets using semi open sets and investigate its basic properties and characterizations in an ideal topological space. This class of sets is properly lies between the class of dI*-closed sets and the class of g-closed sets. Also, study the relationship with various existing closed sets in ideal topological spaces. Moreover, we introduce and study the concept of maximal gsdI*-closed sets

References

S. P. Arya, T. Nour, Characterizations of S-normal Spaces, Indian J. Pure Appl. Math., 21 (8), 717 - 719. 1990.

P. Bhattacharya, B. K. Lahiri, Semi-generalized Closed Sets in Topology, Indian J. Math., 29, 375 – 38. 1987.

J. Dontchev, M. Ganster.,D.Rose, Ideal Resolvability. Topology and its Appl., 93, pp.1-16. 1999.

D. Jonkovic, T.R. Hamlett, New Topologies from old via Ideals, Amer.Math.,Monthly 97, pp. 295-310. 1990.

K. Kuratowski, Topology, Vol. I. New York: Academic Press, 1996.

N. Levine, Generalized Closed Sets in Topology, Rend. Circ. Mat. Palermo., 19, 89 - 96. 1970.

N. Levine, Semiopen Sets and Semi continuity in Topological Spaces, Amer. Math. Monthly,70, 36 - 41.1963.

H. Maki, R. Devi and K. Balachandran, Generalized -closed sets in Topology, Bull. Fukuoka Uni., Ed part III, 13 - 21. 1993.

H. Maki, R. Devi and K. Balachandran, Associated Topologies of Generalized -closedSetsand -generalized Closed Sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 15, 57 – 63. 1994.

M.N. Mukherjee, R. Bishwambhar, R. Sen, On Extension of Topological Spaces in terms of Ideals. Topology and its Appl., 154, pp. 3167-3172, 2007.

B.M. Munshi and D. S. Bassan, Superc continuous Mappings, Indian J. Pure Appl. Math., 13, 229 – 236, 1982.

A.A. Nasef, Rearmament, Some Applications via Fuzzy ideals. Chaos, Solitons and Fractals 13, pp. 825-831, 2002.

M. Navaneethakrishnan, J. Paulraj Joseph, g-closed sets in ideal Topological Spaces, Acta. Math. Hungar., DOI.10.107/s10474-007-7050-1.

O. Njastad, On Some Classes of Nearly Open Sets, Pacific J. Math., 15 (3), 961 –970. 1965.

T. Noiri, On -continuous Functions, J. Korean Math. Soc., 16, pp 161 – 166, 1980.

K. Palani, Karthigaijothi, δI*-Closed sets in Ideal Topological Spaces- Chap. II-Ph.d –Mini Project.

K. Palani, Karthigaijothi, Generalization of δI*-Closed Sets in Ideal Topological Spaces – Ph.d Mini Project – Chap. III.

V. Vaidyanathaswamy, The Localization Theory in set Topology, Proc. Indian.Acad. Sci. 20, 1945.

N.V. Velicko, H-Closed Topological Spaces, Math. Sb.,70, pp. 98-112, 1996.

M.K.R.S. Veerakumar, On ĝ –closed sets in Topological Spaces, Bull.Allh.Math. Soc., 99 – 112. 2003.

S. Yuksel, A. Acikgoz, T. Noiri, On δ-I-Continuous Functions, Turk J Math, 29, pp.39-51, 2005.

Downloads

Published

2022-12-11

Issue

Vol. 44 (2022): Special Issue: Recent Trends in Mathematics and its Applications

Section

Volume 45-2023

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.