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.
Citation
Valentin GUTEV. "Approaching points by continuous selections." J. Math. Soc. Japan 58 (4) 1203 - 1210, October, 2006. https://doi.org/10.2969/jmsj/1179759545
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