Generalized w* -closed sets in bitopological spaces | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 23, Issue 3, 2015, Pages 527-534 PDF (594.57 K) | ||
| Document Type: Original Article | ||
| DOI: 10.1016/j.joems.2014.12.005 | ||
| Authors | ||
| H.M. Abu Donia* 1; M.A. Abd Allah2; A.S. Nawar2 | ||
| 1Department of Mathematics, Faculty of Science, Zagazig University, Egypt | ||
| 2Department of Mathematics, Faculty of Science, Minoufia University, Egypt | ||
| Abstract | ||
| In this paper, we introduce and study a new class of sets in a bitopological space (X, s1, s2), namely, ij-w* -closed sets, which settled properly in between the class of ji-a-closed sets and the class of ij-ga-closed sets. We also introduce and study new classes of spaces, namely, ij T1=5 spaces, ij-Te spaces, ij-aTe spaces, ij-Tl spaces and ij-aTl spaces. As applications of ij-w* -closed sets, we introduce and study four new classes of spaces, namely, ij Tw 1=5 spaces, ij w T1=5 spaces (both classes contain the class of ij T1=5 spaces), ij-aTk spaces and ij-Tk spaces. The class of ij-Tk spaces is properly placed in between the class of ij-Te spaces and the class of ij-Tl spaces. It is shown that dual of the class of ij Tw 1=5 spaces to the class of ij-aTe spaces is the class of ij-aTk spaces and the dual of the class of ij w T1=5 spaces to the class of ij T1=5 spaces is the class of ij Tw 1=5 spaces and also that the dual of the class of ij-Tl spaces to the class of ij-Tk spaces is the class of ij-aTk spaces. Further we introduce and study ij-w* -continuous functions and ij-w* -irresolute functions. | ||
| Keywords | ||
| KEYWORDS ij-w* -closed sets; ij-w* -continuous functions; ij T1=5 spaces; ij T w 1=5 spaces; ij w T1=5 spaces | ||
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