On the metrizability of the hyperspace of nontrivial convergent sequences (Q6546620)

The hyperspace of nontrivial convergent sequences of a topological Hausdorff space \(X\) is denoted by \(S_{c}(X)\). This hyperspace is endowed with the Vietoris topology. In this paper, the authors study the property of metrizability in the view of \(S_{c}(X)\). They prove the main result which states that the hyperspace \(S_{c}(X)\) is metrizable if and only if the ground space \(X\) is also metrizable. As a consequence, they present classes of spaces \(X\) where some generalized metric properties are equivalent for the hyperspace \(S_{c}(X)\).