Open problems in continuum theory problem 1

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Problem 1 (OPICT): Does every nonseparating plane (tree-like) continuum have the fixed-point property?

Answer: Unknown.

For more information see the following survey paper: C. L. Hagopian, Fixed-point problems in continuum theory, Continuum theory and dynamical systems (Arcata, CA, 1989), 79-86, Contemp. Math., 117, Amer. Math. Soc., Providence, RI, 1991.

An essay about this problem by Charles L. Hagopian