On partitions in cylinders over continua and a question of Krasinkiewicz

Volume 122 / 2011

Mirosława Reńska Colloquium Mathematicum 122 (2011), 203-214 MSC: Primary 54F15. DOI: 10.4064/cm122-2-5


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 $X\times I$ such that $L$ is a hereditarily indecomposable continuum. We answer this question in the negative. We also present a construction of such partitions for any continuum $X$ which, for every $\epsilon > 0$, admits a confluent $\epsilon $-mapping onto a locally connected continuum.


  • Mirosława ReńskaInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland

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