New Note on Maximal E-Open and E-Semi- Maximal Open Sets in Topological Spaces

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-49 Number-5
Year of Publication : 2017
Authors : Bishnupada Debnath
  10.14445/22315373/IJMTT-V49P548

MLA

Bishnupada Debnath "New Note on Maximal E-Open and E-Semi- Maximal Open Sets in Topological Spaces", International Journal of Mathematics Trends and Technology (IJMTT). V49(5):307-310 September 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
E. Ekici [8] introduced e-open (resp. eclosed) sets in general topology. Thereafter Nakaoka and Oda ([1] and [2]) initiated the notion of maximal open (resp. minimal closed) sets in topological spaces. In the present work, the author introduces new classes of open and closed sets called maximal e-open sets, minimal e-closed sets, esemi maximal open and e-semi minimal closed and investigate some of their fundamental properties with example and counter examples.

Reference
[1] F. Nakaoka and N. Oda, “Some applications of minimal open sets”, Int. J. Math. Math. Sci. 27 (2001), no. 8, 471- 476.
[2] F. Nakaoka and N. Oda, “Some properties of maximal open sets”, Int. J. Math. Math. Sci. 21(2003), 1331- 1340.
[3] N. V. Velicko, “H-closed topological spaces”, Mat. Sb. (N.S.) 70(112) (1966), 98-112.
[4] J. Cao, M. Ganster, I. Reilly and M. Steiner, “δ-closure,θ- closure and Generalized Closed sets”, Applied General Topology, Vol. 6 (2005), No. 1, 79-86.
[5] N. Levine, Generalized closed sets in topology. Rendiconti del Circ. Math. Di Palermo, Vol. 19(1970) , 89-96. “Amer. Math. Monthly”, 70, 36 – 41 (1963).
[6] S.Raychaudhuri and M.N. Mukherjee, “On δ-almost continuity and δ-preopen sets”, Bull. Inst. Math. Acad. Sincia, 21, 357-366 (1993).
[7] J.H. Park, B.Y. Lee and M.J. Son, “On δ-semiopen sets in topological spaces”, J. Indian Acad. Math., 19(1), 59-67 (1997).
[8] E. Ekici, “ On e-open sets, DP*-sets and DPε *-sets and decompositions of continuity” Arabian J. for Sci. and Engg. in press.

Keywords
δ-open, δ-open, maximal e-open, minimal e-closed, e-semi maximal open and e-semi minimal closed sets.