A complete classification of homogeneous plane continua

We show that every non-degenerate homogeneous plane continuum is homeomorphic to either the unit circle, the pseudo-arc, or the circle of pseudo-arcs. It follows that any planar homogenous compactum has the form \(X \times Z\), where \(X\) is a either a point or one of these three homogeneous plane...

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Bibliographic Details
Published in:arXiv.org 2016-08
Main Authors: Hoehn, L C, Oversteegen, L G
Format: Article
Language:English
Subjects:
Circles (geometry)
Online Access:Get full text
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Summary:We show that every non-degenerate homogeneous plane continuum is homeomorphic to either the unit circle, the pseudo-arc, or the circle of pseudo-arcs. It follows that any planar homogenous compactum has the form \(X \times Z\), where \(X\) is a either a point or one of these three homogeneous plane continua, and \(Z\) is a finite set or the Cantor set. The main technical result in this paper is a new characterization of the pseudo-arc: a non-degenerate continuum is homeomorphic to the pseudo-arc if and only if it is hereditarily indecomposable and has span zero.
ISSN:2331-8422