Hausdorff hypercubes which do not contain arcless continua
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- by Michel Smith PDF
- Proc. Amer. Math. Soc. 95 (1985), 109-114 Request permission
Abstract:
A Hausdorff arc is a compact connected Hausdorff space with exactly two noncut points. The finite product of a Hausdorff arc is called a Hausdorff hypercube. Suppose that $X$ is a Hausdorff arc which is first countable at none of its points and $n$ is a positive integer. We show that every nondegenerate subcontinuum of ${X^n}$ contains a Hausdorff arc. Thus ${X^n}$ contains no nondegenerate hereditarily indecomposable continuum.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 109-114
- MSC: Primary 54F20; Secondary 54B10
- DOI: https://doi.org/10.1090/S0002-9939-1985-0796457-9
- MathSciNet review: 796457