On partitions in cylinders over continua and a question of Krasinkiewicz

Mirosława Reńska

Colloquium Mathematicae (2011)

  • Volume: 122, Issue: 2, page 203-214
  • ISSN: 0010-1354

Abstract

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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 of such partitions for any continuum X which, for every ϵ > 0, admits a confluent ϵ -mapping onto a locally connected continuum.

How to cite

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Mirosława Reńska. "On partitions in cylinders over continua and a question of Krasinkiewicz." Colloquium Mathematicae 122.2 (2011): 203-214. <http://eudml.org/doc/284121>.

@article{MirosławaReńska2011,
abstract = { 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 of such partitions for any continuum X which, for every ϵ > 0, admits a confluent ϵ -mapping onto a locally connected continuum. },
author = {Mirosława Reńska},
journal = {Colloquium Mathematicae},
keywords = {hereditarily indecomposable continua; confluent mappings; locally connected continua; property of Kelley},
language = {eng},
number = {2},
pages = {203-214},
title = {On partitions in cylinders over continua and a question of Krasinkiewicz},
url = {http://eudml.org/doc/284121},
volume = {122},
year = {2011},
}

TY - JOUR
AU - Mirosława Reńska
TI - On partitions in cylinders over continua and a question of Krasinkiewicz
JO - Colloquium Mathematicae
PY - 2011
VL - 122
IS - 2
SP - 203
EP - 214
AB - 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 of such partitions for any continuum X which, for every ϵ > 0, admits a confluent ϵ -mapping onto a locally connected continuum.
LA - eng
KW - hereditarily indecomposable continua; confluent mappings; locally connected continua; property of Kelley
UR - http://eudml.org/doc/284121
ER -

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