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July 2017 Selections and deleted symmetric products
David Buhagiar, Valentin Gutev
Tsukuba J. Math. 41(1): 1-20 (July 2017). DOI: 10.21099/tkbjm/1506353557

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.

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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

Received: 14 January 2016; Revised: 9 June 2017; Published: July 2017
First available in Project Euclid: 25 September 2017

zbMATH: 1383.54016
MathSciNet: MR3705772
Digital Object Identifier: 10.21099/tkbjm/1506353557

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Rights: Copyright © 2017 University of Tsukuba, Institute of Mathematics

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Vol.41 • No. 1 • July 2017
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