Assume is compact, non-empty, perfect, and homeomorphic to its Cartesian square, . Must be homeomorphic to the Cantor set, the Hilbert Cube, or some combination of them?

Hints are appreciated.

Thanks

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- August 15th 2007, 09:55 AMshilz222Compactness
Assume is compact, non-empty, perfect, and homeomorphic to its Cartesian square, . Must be homeomorphic to the Cantor set, the Hilbert Cube, or some combination of them?

Hints are appreciated.

Thanks - August 15th 2007, 11:43 AMshilz222
I think that must be homeomorphic to a combination of the two.

- August 15th 2007, 07:15 PMshilz222
Is this a hard problem in general?

- August 15th 2007, 08:12 PMJakeD
- August 16th 2007, 06:00 AMtopsquark
To be honest, I know I'm curious as to how shilz222 is going to combine the Cantor set and the Hilbert cube...

-Dan