On partitions in cylinders over continua and a question of Krasinkiewicz

• Autorzy: Mirosława Reńska
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54F15: Continua and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 122
• Numer: 2
• Strony: 203-214

Daty

wydano

2011

Twórcy

autor

Mirosława Reńska

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

Identyfikatory

DOI

10.4064/cm122-2-5