The subcontinua of a dendron form a Hilbert cube factor

West, James E.

doi:10.1090/S0002-9939-1972-0312449-9

The subcontinua of a dendron form a Hilbert cube factor
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Proc. Amer. Math. Soc. 36 (1972), 603-608 Request permission

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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The Hilbert cube as a product of dendrons

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The hyperspace of the unit interval

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