{
  "id": "1510.03788",
  "version": "v1",
  "published": "2015-10-13T17:26:55.000Z",
  "updated": "2015-10-13T17:26:55.000Z",
  "title": "Connectedness like properties on the hyperspace of convergent sequences",
  "authors": [
    "S. Garcia-Ferreira",
    "R. Rojas-Hernandez"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-13T17:26:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nontrivial convergent sequences",
      "local connectedness",
      "path-wise connectedness",
      "vietoris hyperspace",
      "warsaw circle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}