Open problems in continuum theory problem 10

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Problem 10 (OPICT): Suppose $M_1,M_2,\ldots$ is a sequence of mutually disjoint continua in the plane converging to the continuum $M$ homeomorphically. Is $M$ circle-like or chainable?

Answer: No. Logan Hoehn, 04-2010, see L. C. Hoehn, An uncountable collection of copies a non-chainable tree-like continuum in the plane, Proc. Amer. Math. Soc. 141 (2013), 2543-2556.