For a topological space X, let \({\mathcal {S}}[X]\) denote the hyperspace of finite unions of convergent sequences endowed with the Pixley–Roy topology. In this paper, we give a characterization of convergent sequences in \({\mathcal {S}}[X]\) . Then we consider some cardinal invariants on \({\mathcal {S}}[X]\) , and compare the character, the pseudocharacter, the sn-character, the cs-character, the cn-character and the ck-character of \({\mathcal {S}}[X]\) with the corresponding cardinal function of X. Moreover, the metrizability and the countable fan tightness of \({\mathcal {S}}[X]\) are discussed. Further, some characterizations of the chain conditions and the weak Lindelöf degree of \({\mathcal {S}}[X]\) are provided.
