Open problems in continuum theory problem 11
Problem 11 (OPICT): Let $X$ be a nondegenerate continuum such that the plane admits a continuous decomposition into topological copies of $X$. Must then $X$ be hereditarily indecomposable? Must $X$ be the pseudo-arc?
Answer: The existence of a continuous decomposition of the plane into pseudo-arcs was announced by R. D. Anderson in 1950. The first known proof of this fact appeared in [W. Lewis and J. J. Walsh, A continuous decomposition of the plane into pseudo-arcs, Houston J. Math. 4 (1978), 209-222].