NEW OPERATORS VIA SEMI-DELTA-OPEN SETS
Kushal Singh1, Asha Gupta2
1,2 Department of Mathematics
Punjab Engineering College
(Deemed to be University)
Chandigarh, 160012 – INDIA

Abstract

Semi-delta-open sets (briefly $\delta_s$-open sets) are a new type of open sets introduced by the authors. The purpose of this paper is to investigate the topological concepts like closure operator, derived set and interior of a set in term of these sets and study their properties. Further, it is shown that the family of semi-delta-open sets forms a topology. In addition, characterizations of semi-delta-open (briefly $\delta_{s}$-open), semi-delta-closed (briefly $\delta_{s}$-closed) and semi -delta-continuous functions (briefly $\delta_{s}$-functions) have been discussed.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 1
Year: 2023

DOI: 10.12732/ijam.v36i1.6

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References

  1. [1] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70, No 1 (1963), 36-41.
  2. [2] N.V. Veliˇcko, H-closed topological spaces, Amer. Math. Soc. Transl., 78 (1968), 103-118.
  3. [3] D.V. Renuka and D. Sivaraj, On -sets in -spaces, Filomat, 22, No 1 (2008), 97-106.
  4. [4] R.M. Latif, Delta-open sets and delta-continuous functions, Int. J. Pure Math., 8 (2021), 1-22.
  5. [5] R.M. Latif, Properties of theta-continuous functions in topological spaces, In: 2020 International Conference on Mathematics and Computers in Sci- ence and Engineering (MACISE), IEEE (2020), 81-90.
  6. [6] J.A. Hassan and M.A. Labendia, s-open sets and s-continuity of maps in the product space, J. Math. Comput. Sci, 25 (2022), 182-190.
  7. [7] S.G. Crossley, Semi-closure, Texas J. Sci., 22 (1971), 99-112.
  8. [8] G. Navalagi and S.V. Gurushantanavar, Some more properties of semi- neighbourhoods in topology, Pacific-Asian J.of Mathematics, 2, No 1-2 (2008), 117-136.
  9. [9] K. Singh and A. Gupta, Semi-delta-open sets in topological space, Bol. Soc. Paran. Mat., doi:10.5269/bspm.62837.
  10. [10] M. Mrˇsevi´c and D. Andrijevi´c, On –connectedness and –closure spaces, Topology Appl., 123, No 1 (2002), 157-166.
  11. [11] R.M. Latif, On characterizations of mappings, Soochow J. Math., 19, No 4 (1993), 475-495.