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We show that a metrizable continuum X is locally connected if and only if every partition in the cylinder over X between the bottom and the top of the cylinder contains a connected partition between these sets.
J. Krasinkiewicz asked whether for every metrizable continuum X there exists a partiton L between the top and the bottom of the cylinder X × I such that L is a hereditarily indecomposable continuum. We answer this question in the negative. We also present a construction...
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