2024/07/23 by Anušić, Ana, Hoehn, Logan C.
#37B45 #37E30 #54C25 #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Primary 54F15 #Secondary 54F50
paper · doi:10.48550/arxiv.2407.16792
We consider the problem of finding embeddings of arc-like continua in the plane for which each point in a given subset is accessible. We establish that, under certain conditions on an inverse system of arcs, there exists a plane embedding of the inverse limit for which each point of a given countable set is accessible. As an application, we show that for any Knaster continuum K, and any countable collection C of composants of K, there exists a plane embedding of K in which every point in the union of the composants in C is accessible. We also exhibit new embeddings of the Knaster buckethandle continuum K in the plane which are attractors of plane homeomorphisms, and for which the restriction of the plane homeomorphism to the attractor is conjugate to a power of the standard shift map on K.