Almost \(e^*\)-continuous functions and their characterizations

Volume 9, Issue 12, pp 6408--6423 http://dx.doi.org/10.22436/jnsa.009.12.40

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1877 Downloads
• 3333 Views

Authors

Burcu Sünbül Ayhan - Faculty of Science, Department of Mathematics, Mugla Sitki Kocman University, 48000 Mentese-Mugla, Turkey. Murad Özkoç - Faculty of Science, Department of Mathematics, Mugla Sitki Kocman University, 48000 Mentese-Mugla, Italy.

Abstract

The main goal of this paper is to introduce and investigate a new class of functions called almost \(e^*\)-continuous functions containing the class of almost e-continuous functions defined by Özkoçand Kına. Several characterizations concerning almost \(e^*\)-continuous functions are obtained. Furthermore, we investigate the relationships between almost \(e^*\)-continuous functions and separation axioms and almost \(e^*\)-closedness of graphs of functions.

Share and Cite

Keywords

• \(e^*\)-open
• \(e^*\)-continuity
• almost \(e^*\)-continuity
• weakly \(e^*\)-continuity
• faintly \(e^*\)-continuity
• \(e^*\)-closed graph.

MSC

•  54C08
•  54C10

References

• [1] D. Andrijević, On b-open sets, Mat. Vesnik, 48 (1996), 59--64


• [2] E. Ekici, New forms of contra-continuity, Carpathian J. Math., 24 (2008), 37--45


• [3] E. Ekici, On a-open sets,\( A^*\)-sets and decompositions of continuity and super-continuity, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 51 (2008), 39--51


• [4] E. Ekici, On e-open sets, \(DP^*\)-sets and \(DPE^*\)-sets and decompositions of continuity, Arab. J. Sci. Eng. Sect. A Sci., 33 (2008), 269--282


• [5] E. Ekici, On \(e^*\)-open sets and \((D; S)^*\)-sets, Math. Morav., 13 (2009), 29--36


• [6] E. Ekici, Some weak forms of \(\delta\)-continuity and \(e^*\)-first-countable spaces, (submitted), (),


• [7] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36--41


• [8] A. S. Mashhour, M. E. Abd El-Monsef, S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47--53


• [9] O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961--970


• [10] T. Noiri, Almost quasi-continuous functions, Bull. Inst. Math. Acad. Sinica, 18 (1990), 321--332


• [11] T. Noiri, V. Popa, On almost \(\beta\)-continuous functions, Acta Math. Hungar., 79 (1998), 329--339


• [12] M. Özkoç, H. Kına, On almost e-continuous functions, (submitted), (),


• [13] J. H. Park, B. Y. Lee, M. J. Son, On \(\delta\)-semiopen sets in topological space, J. Indian Acad. Math., 19 (1997), 59--67


• [14] S. Raychaudhuri, M. N. Mukherjee, On \(\delta\)-almost continuity and \(\delta\)-preopen sets, Bull. Inst. Math. Acad. Sinica, 21 (1993), 357--366


• [15] U. Şengül, On almost b-continuous functions, Int. J. Contemp. Math. Sci., 3 (2008), 1469--1480


• [16] M. K. Singal, S. Prabha Arya, On almost-regular spaces, Glasnik Mat. Ser. III, 4 (1969), 89--99


• [17] M. K. Singal, A. R. Singal, Almost-continuous mappings, Yokohama Math. J., 16 (1968), 63--73


• [18] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 375--381


• [19] S. S. Thakur, P. Paik, Almost \(\alpha\)-continuous mappings, J. Sci. Res., 9 (1987), 37--40


• [20] N. V. Veličko, H-closed topological spaces, Amer. Math. Soc. Transl., 78 (1968), 103--118