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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Weakly smooth continua

Author: Lewis Lum
Journal: Trans. Amer. Math. Soc. 214 (1975), 153-167
MSC: Primary 54F20
MathSciNet review: 0385820
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Abstract: We define and investigate a class of continua called weakly smooth. Smooth dendroids, weakly smooth dendroids, generalized trees, and smooth continua are all examples of weakly smooth continua. We generalize characterizations of the above mentioned examples to weakly smooth continua. In particular, we characterize them as compact Hausdorff spaces which admit a quasi order satisfying certain properties.

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Keywords: Hereditarily unicoherent at a point, indecomposable continuum, irreducible continuum, partial order, quasi order, smooth continuum, type <!– MATH ${\text {A}}’$ –> <IMG WIDTH="26" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="${\text {A}}’$">, weak cut point order, weakly smooth continuum
Article copyright: © Copyright 1975 American Mathematical Society