Connectedness like properties on the hyperspace of convergent sequences release_osp2sq4oujcn7c4artfzcqmq44

by S. Garcia-Ferreira, R. Rojas-Hernandez

Abstract

This paper is a continuation of the work done in sal-yas and may-pat-rob. We deal with the Vietoris hyperspace of all nontrivial convergent sequences S_c(X) of a space X. We answer some questions in sal-yas and generalize several results in may-pat-rob. 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 space of nontrivial convergent sequences on the Warsaw circle has c-many path-wise connected components, and provide a dendroid with the same property.
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Release Date 2015-10-13
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Date   2015-10-13
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arXiv  1510.03788v1
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