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:arXiv.org 2018-12
Main Authors: Hoehn, L C, Oversteegen, L G
Format: Article
Language:English
Subjects:
Equivalence
Online Access:Get full text
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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:2331-8422