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This paper is a continuation of the work done in [3] and [7]. We deal with the Vietoris hyperspace of all nontrivial convergent sequences Sc(X) of a space X. We answer some questions in [3] and generalize several results in [7]. We prove that: The connectedness of X implies the connectedness of Sc(X); the local connectedness of X is equivalent to the local connectedness of Sc(X); and the path-wise...
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