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.
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I think that must be homeomorphic to a combination of the two.
Is this a hard problem in general?
Originally Posted by shilz222 Is this a hard problem in general? It demands some level of mathematical sophistication.
If you want to try out the proof of the answer you gave, I think there are people here who will be able to critique it.
To be honest, I know I'm curious as to how shilz222 is going to combine the Cantor set and the Hilbert cube...
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