A short proof of the nonhomogeneity of the pseudo-circle
by
Kevin Gammon
Auburn University
Coauthors: Krystyna Kuperberg

The pseudo-circle is known to be non-homogeneous. The original proofs of this fact were discovered independently by L. Fearnley in 1969 and J. Rogers 1970. Rogers also proved in 1981 that a homogeneous planar continuum separating the plane is decomposable.

The purpose of this presentation is to provide an alternative, very short proof based on a result of D. Bellamy and W. Lewis which states that a two point Hausdorff compactification of the infinite, connected covering space of a pseudo-circle is a pseudo-arc. In relation to the methods used in the proof, the presenter will also make additional comments on the structure of the lift of crooked chains to both finite and infinite connected covering spaces of the pseudo-circle.

Date received: February 21, 2008