A topological space X is an S-paracompact if there exists a bijective function f from X onto a paracompact space Y such that for every separable subspace A of X the restriction map f | A from A onto f (A) is a homeomorphism. Moreover, if Y is Hausdorff, then X is called S 2-paracompact. We investigate these two properties.

We present new results regarding S2-paracompactness, that we estab-lished in [1], and its relation with other properties such as S-normality, epinormality and L-paracompactness.