Another fixed point theorem for plane continua

Abstract:

A continuum $M$ is said to be $\lambda$ connected if every two points of $M$ can be joined by a hereditarily decomposable subcontinuum of $M$. Here we prove that a bounded plane continuum that does not have infinitely many complementary domains is $\lambda$ connected if and only if its boundary does not contain an indecomposable continuum. It follows that every $\lambda$ connected bounded nonseparating subcontinuum of the plane has the fixed point property.