BIOPERATIONS ON $\alpha$-SEMIOPEN SETS

Abstract

The aim of this paper is to introduce and study the concept of $\alpha_{[\gamma, \gamma^{'}]}$-semiopen sets. Using this set, we introduce and study the concept of $(\alpha_{[\gamma, \gamma^{'}]}, \alpha_{[\beta, \beta^{'}]})$-semicontinuous and $(\alpha_{[\gamma, \gamma^{'}]}, \alpha_{[\beta, \beta^{'}]})$-irresolute functions.

Keywords

• Bioperations,$\alpha$-open set,$\alpha_{,\gamma \gamma^{'},}$-open set,\gamma \gamma^{'},}$-semiopen set

References

1. [1] A. B. Khalaf, S. Jafari and H. Z. Ibrahim, Bioperations on -open sets in topological spaces, International Journal of Pure and Applied Mathematics, 103 (2015), no. 4, 653-666.
2. [2] H. Z. Ibrahim, On a class of $\alpha$-open sets in a topological space, Acta Scientiarum. Technology, 35 (2013), no. 3, 539-545.
3. [3] O. Njastad, On some classes of nearly open sets, Pacic J. Math., 15 (1965), 961-970.
4. [4] N. Levine, semiopen sets and semicontinuity in Topological Spaces, Amer. Math. Monthly, 70 (1963), 36-41.
5. [5] H. Maki and T. Noiri, Bioperations and some separation axioms, Scientiae Mathematicae Japonicae Online, 4 (2001), 165-180.