Hereditarily indecomposable subcontinua of inverse limits of Souslin arcs are metric |
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Authors: | Michel Smith |
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Institution: | Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA |
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Abstract: | We prove that if Si is a Souslin arc (a Hausdorff arc that is the compactification of a Souslin line) for each i and , 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. |
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Keywords: | 54F20 54F15 |
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