On the metrizability of the hyperspace of nontrivial convergent sequences
Keywords:
cosmic space, $G_\delta$-diagonal, hyperspace of nontrivial convergent sequences, metrizability, second countable, separable, $\sigma$-space, stratifiable space, perfectly normalAbstract
The hyperspace of the nontrivial convergent sequences of a topological space Hausdorff $X$ is denoted by $\mathcal{S}_c(X)$. This hyperspace is endowed with the Vietoris topology. In this paper, we show that the the hyperspace $\mathcal{S}_c(X)$ is metrizable if and only if the ground space $X$ possesses the same property.
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