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Space which able to contains higher-dimensional object.

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Let say there are space which able to contains 5-D object completely. Would that means the space itself is actually 6-D ?
 
No for the same reason that a room isn't 4-dimensional for holding a human. The space is just larger than the object to an unknown degree.
So space which able to contain 5-D does not necessary mean 6-D.

But 6-D space able to contain 5-D. Is that correct ?
 
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