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arXiv · 1409.6324

A complete classification of homogeneous plane continua

L. C. Hoehn·L. G. Oversteegen
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Abstract

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.

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L. C. Hoehn, L. G. Oversteegen. 2014-09-22. A complete classification of homogeneous plane continua. https://arxiv.org/abs/1409.6324

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