Hyperspace of finite unions of convergent sequences

The symbol S( X ) denotes the hyperspace of finite unions convergent sequences in a Hausdor˛ space . This hyper-space is endowed with Vietoris topology. First all, we give characterization sequence ). Then consider some cardinal invariants on ), and compare character, pseudocharacter, sn-character, so-character, network weight cs-network S ( corresponding function Moreover, rank k -diagonal 2 such that does not G δ -diagonal. Further, study relations generalized metric properties its Finally, pose questions about