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Transactions of the American Mathematical Society

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



Some special decompositions of $ E\sp{3}$

Author: Charles D. Bass
Journal: Trans. Amer. Math. Soc. 216 (1976), 115-130
MSC: Primary 57A10; Secondary 54B15
MathSciNet review: 0405425
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Abstract: A great deal of attention has been given to the question: which upper semicontinuous decompositions of $ {E^3}$ into pointlike continua give $ {E^3}$. It has recently been determined that some decompositions of $ {E^3}$ into points and straight line segments give decomposition spaces which are topologically distinct from $ {E^3}$. In this paper we apply a new condition to the set of nondegenerate elements of a decomposition which enables one to conclude that the resulting decomposition space is homeomorphic to $ {E^3}$.

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Keywords: Upper semicontinuous decomposition, pointlike, $ {E^3}$, universally monotone set, vertical diameter, $ \varepsilon $-compression, shrinkable collection
Article copyright: © Copyright 1976 American Mathematical Society

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