Inverse Limits of Hausdorff Arcs
Keywords:
continua, indecomposable continua, hereditarily indecomposable continua, Hausdorff spaces, Souslin HypothesisAbstract
We prove that if $\mathbf{X}$ is an inverse limit of Hausdorff arcs and $\mathbf{X}$ is a hereditarily indecomposable continuum, then each coordinate arc has countable cellularity (satisfies the countable chain condition). From this theorem and previous results it follows that if $\mathbf{X}$ is an inverse limit of Hausdorff arcs and $M \subset \mathbf{X}$ is a hereditarily indecomposable continuum, then $M$ is a metric continuum.
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