Stable extensions of homeomorphisms on the pseudo-arc

Abstract:

We prove the following: Theorem. If $P’$ is a proper subcontinuum of the pseudoarc $P, h’$ is a homeomorphism from $P’$ onto itself, and $\Theta$ is an open set in $P$ that contains $P’$, then there is a homeomorphism $h$ from $P$ onto itself such that $h|P’ = h’$ and $h(x) = x$ for $x \notin \Theta$.