Abstract
We give a very simple example of a connected second countable space $X$ whose hyperspace $[X]^{n+1}$ of unordered $(n + 1)$-tuples of points has a continuous selection, but $[X]^n$ has none. This settles an open question posed by Michael Hrušák and Ivan Martánez-Ruiz. The substantial part of the paper sheds some light on this phenomenon by showing that in the presence of connectedness this is essentially the only possible example of such spaces.
Citation
David Buhagiar. Valentin Gutev. "Selections and deleted symmetric products." Tsukuba J. Math. 41 (1) 1 - 20, July 2017. https://doi.org/10.21099/tkbjm/1506353557
Information