Relationship between open sets with respect to an ideal

In this article, we obtain the relationship between the open sets with respect to an ideal defined by [ Michael, F. I., On some open sets with respect to an ideal, Eur. J. Pure Appl. Math, 6 (2013), No. 1, 53–58.], [Rodyna, A. Hosny and Deena, Al-Kadi, Types of Generalized Open Sets with Ideal, Int J Comput Appl., 80 (2013), No. 4, 97-112.], [Rodyna, A. Hosny, Pre-open sets respect ideal, Eur. J. Sci. Res., 104 (2013), No. 1, 99–101.], and the open sets with respect to an ideal defined by [Rosas, E., Carpintero, C., Munoz, A., Pacheco, J., ˜ Some Remarks on Semi Open Sets with Respect to an Ideal, Eur. J. Pure Appl. Math, 7 (2014), No. 4, 437–441.] and [Arafa A. N., Mareay, R. Michael, F. I., Idealization of Some Topological Concepts, Eur. J. Pure Appl. Math, 8 (2015), No. 3, 389–394.]. Also we introduce another class of open sets with respect to an ideal called –-open set and we give the relationships between the three last one.