More monotone open homogeneous locally connected plane continua

Abstract

This paper constructs a continuous decomposition of the Sierpi\'nski curve into acyclic continua one of which is an arc. This decomposition is then used to construct another continuous decomposition of the Sierpi\'nski curve. The resulting decomposition space is homeomorphic to the continuum obtained from taking the Sierpi\'nski curve and identifying two points on the boundary of one of its complementary domains. This outcome is shown to imply that there are continuum many topologically different one dimensional locally connected plane continua that are homogeneous with respect to monotone open maps.