On the descriptive complexity of homogeneous continua

It is shown that the family of all homogeneous continua in the hyperspace of all subcontinua of any finite-dimensional Euclidean cube or the Hilbert cube is an analytic subspace of the hyperspace which contains a topological copy of the linear space \(c_0=\{(x_k)\in \mathbb R^\omega: \lim x_k=0\}\)...

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Bibliographic Details
Published in:arXiv.org 2021-03
Main Author: Krupski, Paweł
Format: Article
Language:English
Subjects:
Euclidean geometry
Hyperspaces
Online Access:Get full text
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Summary:It is shown that the family of all homogeneous continua in the hyperspace of all subcontinua of any finite-dimensional Euclidean cube or the Hilbert cube is an analytic subspace of the hyperspace which contains a topological copy of the linear space \(c_0=\{(x_k)\in \mathbb R^\omega: \lim x_k=0\}\) as a closed subset.
ISSN:2331-8422
DOI:10.48550/arxiv.2103.01202