Hereditarily indecomposable subcontinua of inverse limits of Souslin arcs are metric

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• 作者：Michel Smith
• 关键词：Indecomposable continuum ; Non-metric continuum ; Lexicographical ordering
• 刊名：Topology and its Applications
• 出版年：2008
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：1 February 2008
• 卷：155
• 期：6
• 页码：540-543
• 文件大小：97 K

摘要

We prove that if S_i is a Souslin arc (a Hausdorff arc that is the compactification of a Souslin line) for each i and 53d2eae9a550260ae93fad050f573b">, then every hereditarily indecomposable subcontinuum of X is metric. Since every non-degenerate hereditarily indecomposable continuum that is an inverse limit on metric arcs is a pseudo-arc, it follows that such an X would be a pseudo-arc or a point.