论文标题
收敛序列有限工会的超空间
Hyperspace of finite unions of convergent sequences
论文作者
论文摘要
符号$ \ MATHCAL {s}（x）$表示Hausdorff空间中有限的收敛序列的超空间。这个超空间已赋予越野拓扑。首先，我们在$ \ Mathcal {s}（x）$中给出收敛序列的表征。然后，我们考虑$ \ Mathcal {s}（x）$上的一些红衣主教不变式，并比较角色，伪character，$ sn $ -character，$ so $ so $ -character，网络重量，网络重量和$ cs $ -network $ -network加权$ \ Mathcal {s} $ a} $ $ x $ $ x $ x $ x $ x $ x $。此外，我们考虑$ \ Mathcal {s}（x）$上的排名$ k $ -diagonal，并给出一个带有等级2-Diagonal的空间$ x $，以至于$ s（x）$没有任何$g_Δ$ -diagonal。此外，我们研究了$ x $的某些广义度量属性及其超空间$ \ mathcal {s}（x）$的关系。最后，我们提出了一些有关超空间$ \ Mathcal {s}（x）$的问题。
The symbol $\mathcal{S}(X)$ 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 $\mathcal{S}(X)$. Then we consider some cardinal invariants on $\mathcal{S}(X)$, and compare the character, the pseudocharacter, the $sn$-character, the $so$-character, the network weight and $cs$-network weight of $\mathcal{S}(X)$ with the corresponding cardinal function of $X$. Moreover, we consider rank $k$-diagonal on $\mathcal{S}(X)$, and give a space $X$ with a rank 2-diagonal such that $S(X)$ does not have any $G_δ$-diagonal. Further, we study the relations of some generalized metric properties of $X$ and its hyperspace $\mathcal{S}(X)$. Finally, we pose some questions about the hyperspace $\mathcal{S}(X)$.
