\(\theta_s\)-open sets and \(\theta_{s}\)-continuity of maps in the product space

Volume 25, Issue 2, pp 182--190 http://dx.doi.org/10.22436/jmcs.025.02.07

Publication Date: May 27, 2021 Submission Date: April 26, 2020 Revision Date: April 03, 2021 Accteptance Date: April 29, 2021

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Authors

Javier A. Hassan - Department of Mathematics \(\&\) Statistics, College of Science \(\&\) Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City, Philippines. Mhelmar A. Labendia - Department of Mathematics \(\&\) Statistics, College of Science \(\&\) Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City, Philippines.

Abstract

In this study, the concept of \(\theta_s\)-open set is introduced. The topology formed by \(\theta_s\)-open sets is strictly finer than the topology formed by \(\theta\)-open sets but is not comparable with the topology formed by \(\omega_\theta\)-open sets. Related concepts such as \(\theta_s\)-open and \(\theta_s\)-closed functions, \(\theta_s\)-continuous function, \(\theta_s\)-connected space, and some versions of separation axioms are defined and characterized. Finally, the concept of \(\theta_s\)-continuous function from an arbitrary topological space into the product space is investigated further.

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Keywords

• \(\theta_s\)-open
• \(\theta_s\)-closed
• \(\theta_s\)-connected
• \(\theta_s\)-continuous
• \(\theta_s\)-Hausdorff
• (\theta_s\)-regular
• \(\theta_s\)-normal

MSC

•  54A10
•  54A05

References

• [1] T. A. Al-Hawary, On supper continuity of topological spaces, MATEMATIKA: Malays. J. Indust. Appl. Math., 21 (2005), 43--49
  • View Article
  • Google Scholar


• [2] H. H. Aljarrah, M. S. M. Noorani, T. Noiri, Contra $\omega\beta$-continuity, Bol. Soc. Parana. Mat. (3), 32 (2014), 9--22
  • View Article
  • MathSciNet
  • Google Scholar


• [3] H. H. Aljarrah, M. S. M. Noorani, T. Noiri, On generalized $\omega\beta$-closed sets, Missouri J. Math. Sci., 26 (2014), 70--87
  • View Article
  • MathSciNet
  • Google Scholar


• [4] K. Al-Zoubi, K. Al-Nashef, The topology of $\omega$-open subsets, Al-Manarah Journal, 9 (2003), 169--179
  • Google Scholar


• [5] M. Caldas, S. Jafari, M. M. Kovar, Some properties of $\theta$-open sets, Divulg. Mat., 12 (2004), 161--169
  • View Article
  • MathSciNet
  • Google Scholar


• [6] M. Caldas, S. Jafari, R. M. Latif, Sobriety via $\theta$-open sets, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 56 (2010), 163--167
  • View Article
  • MathSciNet


• [7] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Properties of faintly $\omega$-continuous functions, Bol. Mat., 20 (2013), 135--143
  • View Article
  • MathSciNet


• [8] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Some properties of upper/lower $\omega$-continuous multifunctions, Sci. Stud. Res. Ser. Math. Inform., 23 (2013), 35--55
  • View Article
  • MathSciNet
  • Google Scholar


• [9] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, On upper and lower almost contra-$\omega$-continuous multifunctions, Ital. J. Pure Appl. Math., 32 (2014), 445--460
  • View Article
  • MathSciNet
  • Google Scholar


• [10] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Somewhat $\omega$-continuous functions, Sarajevo J. Math., 11 (2015), 131--137
  • View Article
  • MathSciNet


• [11] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Upper and lower $\omega$-continuous multifunctions, Afr. Mat., 26 (2015), 399--405
  • View Article
  • MathSciNet


• [12] H. M. Darwesh, Between preopen and open sets in topological spaces, Thai J. Math., 11 (2013), 143--155
  • View Article
  • MathSciNet
  • Google Scholar


• [13] R. F. Dickman, J. R. Porter, $\theta$-closed subsets of Hausdorff spaces, Pacific J. Math., 59 (1975), 407--415
  • View Article
  • MathSciNet


• [14] R. F. Dickman, J. R. Porter, $\theta$-perfect and $\theta$-absolutely closed functions, Illinois J. Math., 21 (1977), 42--60
  • View Article
  • MathSciNet
  • Google Scholar


• [15] E. Ekici, S. Jafari, R. M. Latif, On a finer topological space than $\tau_\theta$ and some maps, Ital. J. Pure Appl. Math., 27 (2010), 293--304
  • MathSciNet
  • Google Scholar


• [16] H. Z. Hdeib, $\omega$-closed mappings, Rev. Colombiana Mat., 16 (1982), 65--78
  • View Article
  • MathSciNet
  • Google Scholar


• [17] D. S. Jankovic, $\theta$-regular spaces, Internat. J. Math. Math. Sci., 8 (1986), 615--619
  • View Article
  • MathSciNet
  • Google Scholar


• [18] J. E. Joseph, $\theta$-closure and $\theta$-subclosed graphs, Math. Chronicle, 8 (1979), 99--117
  • MathSciNet


• [19] M. M. Kovár, On $\theta$-regular spaces, Internat. J. Math. Math. Sci., 17 (1994), 687--692
  • View Article
  • MathSciNet
  • Google Scholar


• [20] M. A. Labendia, J. A. C. Sasam, On $\omega$-connectedness and $\omega$-continuity in the product space, Eur. J. Pure Appl. Math., 11 (2018), 834--843
  • View Article
  • MathSciNet
  • Google Scholar


• [21] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36--41
  • View Article
  • MathSciNet
  • Google Scholar


• [22] P. E. Long, L. L. Herrington, The $\tau_\theta$-topology and faintly continuous functions, Kyungpook Math. J., 22 (1982), 7--14
  • View Article
  • Google Scholar


• [23] T. Noiri, S. Jafari, Properties of $(\theta,s)$-continuous functions, Topology Appl., 123 (2002), 167--179
  • View Article
  • MathSciNet


• [24] N. Veličko, $H$-closed topological spaces, (Russian) Mat. Sb. (N.S.), 70 (1966), 98--112
  • View Article
  • MathSciNet
  • Google Scholar