The universality property for some new classes of spaces

The notion of saturated class of spaces is given by S.D. Iliadis in [5]. In the saturated classes there are universal elements. However, the saturated classes of spaces have “something more” than the existence of universal elements. For example, the intersection of saturated classes is also a saturated class while the intersection of classes of spaces having universal elements does not have in general such elements.We introduce some new classes of topological spaces in which there exist universal elements. In fact we will prove that the new classes are saturated. These classes are more general than known classes, such as the class of extremally disconnected spaces and the class of GδGδ-spaces.