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Displaying similar documents to “Complexity of curves”

On partitions in cylinders over continua and a question of Krasinkiewicz

Mirosława Reńska (2011)

Colloquium Mathematicae

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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...

Non-separating subcontinua of planar continua

D. Daniel, C. Islas, R. Leonel, E. D. Tymchatyn (2015)

Colloquium Mathematicae

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We revisit an old question of Knaster by demonstrating that each non-degenerate plane hereditarily unicoherent continuum X contains a proper, non-degenerate subcontinuum which does not separate X.