Planar embeddings of Minc's continuum and generalizations

2020/10/06 by Ana Anušić, Anušić, Ana
Mathematics · #37B45 #37C70 #37E05 #54C25 #54F15 #54H20 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:37B45 #msc:37C70 #msc:37E05 #msc:54C25 #msc:54F15 #msc:54H20

paper · pdf · doi:10.48550/arxiv.2010.02969

15 pages, 8 figures

arxiv created 2020/10/06 · arxiv updated 2020/10/08

Abstract

We show that if f\colon I→ I is piecewise monotone, post-critically finite, and locally eventually onto, then for every point x∈ X=\underleftarrowlim(I,f) there exists a planar embedding of X such that x is accessible. In particular, every point x in Minc's continuum X_M from [Question 19 p. 335 in Continuum theory : proceedings of the special session in honor of Professor Sam B. Nadler, Jr.'s 60th birthday, Lecture notes in pure and applied mathematics; v. 230, New York: Marcel Dekker.] can be embedded accessibly. All constructed embeddings are thin, i.e. can be covered by an arbitrary small chain of open sets which are connected in the plane.

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