Contractibility of the hyperspace of sequences, harmonic fan

Given a Hausdorff space X, let Sc(X) be the hyperspace of nontrivial convergent sequences. It is an open problem to determine if the contractibility of X implies the contractibility of Sc(X). In this paper we prove that if X is the harmonic fan, then Sc(X) is contractible. We also prove that the con...

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Veröffentlicht in:	Topology and its applications 2020-05, Vol.277, p.107167, Article 107167
1. Verfasser:	Illanes, Alejandro
Format:	Artikel
Sprache:	eng
Schlagworte:	Continuum Contractibility Dendrite Harmonic fan Hyperspace Hyperspace of nontrivial sequences
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Zusammenfassung:	Given a Hausdorff space X, let Sc(X) be the hyperspace of nontrivial convergent sequences. It is an open problem to determine if the contractibility of X implies the contractibility of Sc(X). In this paper we prove that if X is the harmonic fan, then Sc(X) is contractible. We also prove that the contractibility of X implies that Sc(X) is pathwise connected. This answers questions by Camargo, Maya and Pellicer-Covarrubias.
ISSN:	0166-8641 1879-3207
DOI:	10.1016/j.topol.2020.107167