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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


The subcontinua of a dendron form a Hilbert cube factor

Author: James E. West
Journal: Proc. Amer. Math. Soc. 36 (1972), 603-608
MSC: Primary 54B20; Secondary 54A20
MathSciNet review: 0312449
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Abstract: The title statement is proved, and it is shown further that the subcontinua of a dendron actually form a Hilbert cube when (and only when) the branch points of the dendron are dense. Along the way, it is established that whenever a Hilbert cube manifold is compactified into a Hilbert cube factor by the addition of another Hilbert cube factor having Property Z in the compactification, then the resulting space is actually a Hilbert cube.

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PII: S 0002-9939(1972)0312449-9
Keywords: Hyperspace of subcontinua, dendron, Hilbert cube, Hilbert cube factor, Hilbert cube manifold, compactification
Article copyright: © Copyright 1972 American Mathematical Society