Connectedness like properties on the hyperspace of convergent sequences.

This paper is a continuation of the work done in [3] and [7] . We deal with the Vietoris hyperspace of all nontrivial convergent sequences S c ( 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 S c ( X ) ; the local connectedness of X is equivalent to the local connectedness of S c ( X ) ; and the path-wise connectedness of S c ( X ) implies the path-wise connectedness of X . We also show that the hyperspace of nontrivial convergent sequences on the Warsaw circle has c -many path-wise connected components, and provide a dendroid with the same property. [ABSTRACT FROM AUTHOR]