The extensionality of ⊤-convergence spaces is verified for a complete residuated lattice L with the top element ⊤. And also the $\mathcal{E}$-connectedness of ⊤-convergence spaces for a class $\mathcal{E}$ of ⊤-convergence spaces is proposed by generalizing Preuss's connectedness of topological spaces. Then we establish a necessary and sufficient condition that for a class $\mathcal{K}$ of ⊤-convergence spaces, there exists a class $\mathcal{E}$ of ⊤-convergence spaces such that each space of $\mathcal{K}$ is $\mathcal{E}$-connected, where we stress the point that the conclusion benefits from the extensionality of the category of ⊤-convergence spaces. We further present a deep relationship between $\mathcal{E}$-connectedness and $T_1$-separation for ⊤-convergence spaces, that is, the $\mathcal{E}$-connectedness of each subset in a ⊤-convergence space implies that of its closure if and only if $\mathcal{E}$ precisely is a class of ⊤-convergence spaces being $T_1$-separated, and as a natural result, the product theorem for $\mathcal{E}$-connected ⊤-convergence spaces is obtained.

⊤-收敛空间的可拓性被验证为一个完全剩余格子L与顶部元素 ⊤。还有$\mathcal{乙}$-类的 ⊤-收敛空间的连通性 $\mathcal{乙}$⊤-收敛空间是通过推广普鲁士拓扑空间的连通性提出的。然后我们建立一个充要条件，对于一个类$\mathcal{钾}$ 在 ⊤-收敛空间中，存在一类 $\mathcal{乙}$ 的 ⊤-收敛空间使得每个空间 $\mathcal{钾}$ 是 $\mathcal{乙}$-connected，这里我们强调结论受益于⊤-收敛空间范畴的可拓性。我们进一步提出了两者之间的深层关系$\mathcal{乙}$- 连通性和 ${吨}_1$-分离⊤-收敛空间，即 $\mathcal{乙}$⊤-收敛空间中每个子集的连通性意味着它的闭包当且仅当 $\mathcal{乙}$ 恰好是一类⊤-收敛空间是 ${吨}_1$- 分离，并且作为自然结果，乘积定理为 $\mathcal{乙}$得到-连通的⊤-收敛空间。