April 2023 ON UNICOHERENCE AND CONTRACTIBILITY OF HYPERSPACES OF NONMETRIZABLE CONTINUA
Luis Miguel García-Velázquez
Rocky Mountain J. Math. 53(2): 435-448 (April 2023). DOI: 10.1216/rmj.2023.53.435

Abstract

Let X be a Hausdorff continuum (a nondegenerate, compact, connected Hausdorff space). Let C(X) denote the hyperspace of its subcontinua, endowed with the Vietoris topology. We extend some results of the metric case about unicoherence and the existence of selections for C(X). We also introduce two definitions of contractibility of C(X) and discuss their relation with some properties of X. In particular, we show that both definitions are equivalent in the metrizable case, but one of them is more general in the Hausdorff continuum case.

Citation

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Luis Miguel García-Velázquez. "ON UNICOHERENCE AND CONTRACTIBILITY OF HYPERSPACES OF NONMETRIZABLE CONTINUA." Rocky Mountain J. Math. 53 (2) 435 - 448, April 2023. https://doi.org/10.1216/rmj.2023.53.435

Information

Received: 22 August 2021; Revised: 14 April 2022; Accepted: 24 May 2022; Published: April 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604765
zbMATH: 07725146
Digital Object Identifier: 10.1216/rmj.2023.53.435

Subjects:
Primary: 54B20
Secondary: 54F15

Keywords: contractibility , Hausdorff continuum , hyperspace , selections , unicoherence , Vietoris topology

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 2 • April 2023
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