DOI QR코드

DOI QR Code

DENSE SETS IN WEAK STRUCTURE AND MINIMAL STRUCTURE

  • Received : 2012.09.14
  • Published : 2013.07.31

Abstract

This paper is an attempt to study and introduce the notion of ${\omega}$-dense set in weak structures and the notion of m-dense set in minimal structures. We have also investigate the relationships between ${\omega}$-dense sets, $m$-dense sets, ${\sigma}({\omega})$ sets, ${\pi}({\omega})$ sets, $r({\omega})$ sets, ${\beta}({\omega})$ sets, m-semiopen sets and $m$-preopen sets. Further we give some representations of the above generalized sets in minimal structures as well as in weak structures.

References

  1. M. Alimohammady and M. Roohi, Fixed point in minimal spaces, Nonlinear Anal. Model. Control 10 (2005), no. 4, 305-314.
  2. M. Alimohammady and M. Roohi, Linear minimal spaces, Chaos Solitons Fractals 33 (2007), no. 4, 1348-1354. https://doi.org/10.1016/j.chaos.2006.01.100
  3. A. Csaszar, Generalized open sets, Acta Math. Hungar. 97 (1997), no. 1-2, 65-87.
  4. A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), no. 4, 351-357. https://doi.org/10.1023/A:1019713018007
  5. A. Csaszar, Weak structures, Acta Math. Hungar. 131 (2011), no. 1-2, 193-195. https://doi.org/10.1007/s10474-010-0020-z
  6. M. Ganster, Preopen sets and resolvable spaces, Kyungpook Math. J. 27 (1987), no. 2, 135-142.
  7. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41. https://doi.org/10.2307/2312781
  8. H. Maki, J. Umehara, and T. Noiri, Every topological space is pre T1/2, Men. Fac. Sci. Kochi Univ. Ser. A Math. 17 (1996), 33-42.
  9. A. S. Mashhour, M. E. AbD El-Mosef, and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47-53.
  10. W. K. Min, m-semiopen sets and M-semicontinuous functions on spaces with minimal structures, Honam Math. J. 31 (2009), no. 2, 239-245. https://doi.org/10.5831/HMJ.2009.31.2.239
  11. W. K. Min, On minimal semicontinuous functions, Commun. Korean Math. Soc. 27 (2012), no. 2, 341-345. https://doi.org/10.4134/CKMS.2012.27.2.341
  12. W. K. Min and Y. K. Kim, On minimal precontinuous functions, J. Chun. Math. Soc. 22 (2009), no. 4, 667-673.
  13. W. K. Min and Y. K. Kim, m-preopen sets and M-precontinuity on spaces with minimal structures, Adv. Fuzzy Sets Syst. 4 (2009), no. 3, 237-245.
  14. O. B. Ozbakir and E. D. Yildirim, On some closed sets in ideal minimal spaces, Acta. Math. Hungar. 125 (1009), no. 3, 227-235.

Cited by

  1. gm-continuity on generalized topology and minimal structure spaces vol.20, 2016, https://doi.org/10.1016/j.jaubas.2014.07.003
  2. ON THE GEOMETRY OF LORENTZ SPACES AS A LIMIT SPACE vol.51, pp.4, 2014, https://doi.org/10.4134/BKMS.2014.51.4.957