Approaching points by continuous selections

  • Gutev Valentin
    School of Mathematical Sciences, Faculty of Science, University of KwaZulu-Natal

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Abstract

Some further results about special Vietoris continuous selections and totally disconnected spaces are obtained, also several applications are demonstrated. In particular, it is demonstrated that a homogeneous separable metrizable space has a continuous selection for its Vietoris hyperspace if and only if it is discrete, or a discrete sum of copies of the Cantor set, or is the irrational numbers.

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