Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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APPLICATIONS OF SEMI-OPEN SETS

  • Bae, Ji-Hye (Department of Mathematics Education (and RINS) Gyeongsang National University) ;
  • Cho, So-Hui (Department of Mathematics Education (and RINS) Gyeongsang National University) ;
  • Jun, Young-Bae (Department of Mathematics Education (and RINS) Gyeongsang National University) ;
  • Kim, Chang-Su (Department of Mathematics Education (and RINS) Gyeongsang National University)
  • Received : 2007.02.01
  • Accepted : 2007.08.22
  • Published : 2007.09.25
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Abstract

The aim of this paper is to introduce and study topological properties of semi-limit points, semi-derived, semi-interior, semi-closure, semi-border, and semi-frontier of a set using the concept of semi-open set.

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References

  1. D. Andrijevic, Some properties of the topology of a-sets, Mat. Vesnik 36 (1984), 1-10.
  2. M. Caldas, A note on some applications of ${\alpha}-sets$, Int. J. Math. Math. Sci. 2003 (2003), no. 2, 125-130. https://doi.org/10.1155/S0161171203203161
  3. M. Caldas and J. Dontchev, On spaces with hereditarily compact ${\alpha}-topologies$, Acta Math. Hung. 82 (1999), 121-129. https://doi.org/10.1023/A:1026450024704
  4. S. Jafari and T. Noiri, $Contra-{\alpha}-continuous$ functions between topological spaces, Iranian Int. J. Sci. 2 (2001), no. 2, 153-167.
  5. S. Jafari and T. Noiri, Some remarks on weak ${\alpha}-continuity$, Far East J. Math. Sci. 6 (1998), no. 4, 619-625.
  6. S. N. Maheshwari and S. S. Thakur, On ${\alpha}-irresolute$ mappings, Tamkang J. Math. 11 (1980), 209-214.
  7. S. N. Maheshwari and S. S. Thakur, On ${\alpha}-compact$ spaces, Bull. Inst. Math. Acad. Sinica 13 (1985), 341-347.
  8. H. Maki, R. Devi and K. Balachandran, Generalized ${\alpha}-closed$ sets in topology, Bull. Fukuoka Univ. Ed. Part III 42 (1993), 13-21.
  9. H. Maki and T. Noiri, The pasting lemma for ${\alpha}-continuous$ maps, Glas. Mat. 23(43) (1988),357-363.
  10. A. S. Mashhour, I. A. Hasanein and S. N. El-Deeb, A note on semi-continuity and precontinuity, Indian J. Pure Appl. Math. 13 (1982), no. 10, 1119-1123.
  11. A. S. Mashhour, I. A. Hasanein and S. N. EI-Deeb, ${\alpha}-continuous$ and ${\alpha}-open$ mappings, Acta Math. Hungar. 41 (1983), no. 3-4, 213-218. https://doi.org/10.1007/BF01961309
  12. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41. https://doi.org/10.2307/2312781
  13. O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970. https://doi.org/10.2140/pjm.1965.15.961
  14. I. L. Reilly and M. K. Vamanamurthy, On ${\alpha}-sets$ in topological spaces, Tamkang J. Math. 16 (1985), 7-11.
  15. J. Tong, On decomposition of continuity in topological spaces, Acta Math. Hungar. 54 (1989), no. 1-2,51-55. https://doi.org/10.1007/BF01950708