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Corrected the title according to the contents of the problem

edited Jan 8, 2017 at 1:06

The anti-symmetric property of the collection of all compact convex sets of a Banach space

Edit: According to comment of " Fedor Petrov", I revise my question

Are there two compact convex subsets $X,Y$ of a Banach space with the following property?

They are not homeomorphic spaces but $X$ can be embedded in $Y$ and $Y $ can be embedded in $X$?

asked Jan 7, 2017 at 14:17