Abstract
Adendroid is an arcwise connected hereditarily unicoherent continuum. Ashore set in a dendroidX is a subsetA ofX such that, for each ε>0, there exists a subdendroidB ofX such that the Hausdorff distance fromB toX is less then ε andB∩A=θ.
Answering a question by I. Puga, in this paper we prove that the finite union of pairwise disjoint shore subdendroids of a dendroidX is a shore set. We also show that the hypothesis that the shore subdendroids are disjoint is necessary. It is still unknown if the union of two closed disjoint shore subsets of a dendroidX is also shore set.
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Bibliography
Charatonik J. J.,Problems and remarks on contractibility of curves, General Topology and its Relations to Modern Analysis and Algebra IV, Proc. Fourth Prague Topological Symposium, (1976); Part B Contributed papers Society of Czechoslovak Mathematicians and Physicists Prague, (1977), 72–76.
Hurewicz W., Wallman H.,Dimension Theory, Princeton University Press ninth printing, (1974).
Illanes A., Nadler S. B. Jr.,Hyperspaces, Fundamentals and Recent Advances, Monographs and Textbooks in Pure and Applied Mathematics,216, Marcel Dekker Inc., (1999).
Montejano-Peimbert L., Puga-Espinosa I.,Shore points in dendroids and conical pointed hyperspaces, Topology Appl.,46 (1992), 41–54.
Neumann-Lara V., Puga-Espinosa I.,Shore points and dendrites, Proc. Amer. Math. Soc.,118 (1993), 939–942.
Neumann-Lara V., Puga-Espinosa I.,Shore points and noncut points in dendroids, Topology Appl.,92 (1999), 183–190.
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Illanes, A. Finite unions of shore sets. Rend. Circ. Mat. Palermo 50, 483–498 (2001). https://doi.org/10.1007/BF02844427
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DOI: https://doi.org/10.1007/BF02844427