| Abstract: |
| Title: \textbf{Inverse Limits of Hausdorff Arc Not Imbeddable in the Product of Two Hausdorff Arcs.}
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Author: Michel Smith
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It is well known that an inverse limit of metric arcs imbeds in the product of two metric arcs. At the other end of the spectrum of inverse limits, an inverse limit of Hausdorff arcs over an index set having no cofinal countable set, is a Hausdorff arc. Though such an arc may not be homeomorphic to any of the coordinate spaces, it trivially imbeds in the product of two Hausdorff arcs. We consider the intermediate situation and show that there exist inverse limits of Hausdorff arcs which are not imbeddable in the product of any two Hausdorff arcs. The index set must be countable and, from previous work of the author, the example cannot contain non-metric hereditarily indecomposable continua. thus they can`t be ``too`` complicated.
Additional questions related to the area will be discussed. |
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