  This paper is a continuation of the work done in \cite{sal-yas} and
\cite{may-pat-rob}. We deal with the Vietoris hyperspace of all nontrivial
convergent sequences $\mathcal{S}_c(X)$ of a space $X$. We answer some
questions in \cite{sal-yas} and generalize several results in
\cite{may-pat-rob}. We prove that: The connectedness of $X$ implies the
connectedness of $\mathcal{S}_c(X)$; the local connectedness of $X$ is
equivalent to the local connectedness of $\mathcal{S}_c(X)$; and the path-wise
connectedness of $\mathcal{S}_c(X)$ implies the path-wise connectedness of $X$.
We also show that the space of nontrivial convergent sequences on the Warsaw
circle has $\mathfrak{c}$-many path-wise connected components, and provide a
dendroid with the same property.
