Bruin–Kolyada–Snoha conjecture on minimal maps of the pseudo-circle
Bruin–Kolyada–Snoha conjecture on minimal maps of the pseudo-circle
Let the pseudo-circle be R.H. Bing's pseudo-circle, an infinite continuum that admits minimal homeomorphisms. A map is noninvertible when it is not a homeomorphism, and a map is minimal when every forward orbit is dense. Bruin–Kolyada–Snoha's conjecture. The pseudo-circle is another continuum that admits minimal homeomorphisms, but no noninvertible minimal maps. The conjecture concerns whether the pseudo-circle could be a counterexample to the question of whether the circle is the only infinite continuum admitting a minimal homeomorphism but no noninvertible minimal map. It is refuted by the paper's construction of a minimal non-invertible map on the pseudo-circle.
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Primary source
Jan P. Boronski, Judy Kennedy, Xiao-Chuan Liu and Piotr Oprocha, “Minimal non-invertible maps on the pseudo-circle”, arXiv:1810.07688 (2019).
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