Approaching points by continuous selections
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.
- Journal of the Mathematical Society of Japan
Journal of the Mathematical Society of Japan 58(4), 1203-1210, 2006-10-01
The Mathematical Society of Japan