2020/05/17 by Jingling Lin, Lin, Jingling, Fucai Lin +3
Mathematics · #54B20 #54D20 #54D25 #54E20 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Primary 54A20 #secondary 54A25
paper · pdf · doi:10.48550/arxiv.2005.08154
openalex publication_date 2020/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The symbol S(X) denotes the hyperspace of finite unions of convergent sequences in a Hausdorff space X. This hyperspace is endowed with the Vietoris topology. First of all, we give a characterization of convergent sequence in S(X). Then we consider some cardinal invariants on S(X), and compare the character, the pseudocharacter, the sn-character, the so-character, the network weight and cs-network weight of S(X) with the corresponding cardinal function of X. Moreover, we consider rank k-diagonal on S(X), and give a space X with a rank 2-diagonal such that S(X) does not have any Gδ-diagonal. Further, we study the relations of some generalized metric properties of X and its hyperspace S(X). Finally, we pose some questions about the hyperspace S(X).