Cardinal invariants and universality

We define and investigate some new cardinal invariants using sums of spaces belonging to a fixed class of spaces. Our approach includes known invariants as special cases, such as the cardinality of a topological space, the number of connected components of a topological space, and the metrizability number, first countability number, discrete metrizability number. Also, we study the problem of universality for some classes of spaces which are defined by the new cardinal invariants. In fact we prove that these classes are saturated. The notion of saturated class of spaces is given by S.D. Iliadis in [7]. 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.