# REMARKS ON γ-OPERATIONS INDUCED BY A TOPOLOGY

• Accepted : 2010.12.14
• Published : 2011.04.30
• 41 3

#### Abstract

Cs$\'{a}$sz$\'{a}$r [3] introduced the notions of ${\gamma}$-compact and ${\gamma}$-operation on a topological space. In this paper, we introduce the notions of almost ${\Gamma}$-compact, (${\gamma},{\tau}$)-continuous function and (${\gamma},{\tau}$)-open function defined by ${\gamma}$-operation on a topological space and investigate some properties for such notions.

#### Keywords

(${\gamma},{\tau}$)-continuous;(${\gamma},{\tau}$)-open;${\Gamma}$-closed graph;strongly ${\Gamma}$-closed graph;${\gamma}$-compact;almost ${\Gamma}$-compact

#### References

1. M. E. Abd El-Monsef, S. N. El-Deeb, and R. A. Mahmoud, $\beta$-open sets and $\beta$-continuous mapping, Bull. Fac. Sci. Assiut Univ. A 12 (1983), no. 1, 77-90.
2. A. Csaszar, Generalized open sets, Acta. Math. Hungar. 75 (1997), no. 1-2, 65-87. https://doi.org/10.1023/A:1006582718102
3. A. Csaszar, $\gamma$-compact spaces, Acta. Math. Hungar. 87 (2000), no. 1-2, 99-107. https://doi.org/10.1023/A:1006725101012
4. A. Csaszar, $\gamma$-compact spaces, Acta. Math. Hungar. 101 (2003), no. 4, 273-279. https://doi.org/10.1023/B:AMHU.0000004939.57085.9e
5. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41. https://doi.org/10.2307/2312781
6. A. S. Mashhour, M. E. Abd El-Monsef, and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. and Phys. Soc. Egypt 53 (1982), 47-53.
7. O. Nj_ astad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970. https://doi.org/10.2140/pjm.1965.15.961
8. N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78 (1968), 103-118.