A complete classification of hereditarily equivalent plane continua

A continuum is hereditarily equivalent if it is homeomorphic to each of its non-degenerate sub-continua. We show in this paper that the arc and the pseudo-arc are the only non-degenerate hereditarily equivalent plane continua.

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2020-07, Vol.368, p.107131, Article 107131
Main Authors: Hoehn, L.C., Oversteegen, L.G.
Format: Article
Language:English
Subjects:
Hereditarily equivalent
Hereditarily indecomposable
Plane continua
Pseudo-arc
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Summary:A continuum is hereditarily equivalent if it is homeomorphic to each of its non-degenerate sub-continua. We show in this paper that the arc and the pseudo-arc are the only non-degenerate hereditarily equivalent plane continua.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2020.107131