The anti-symmetric property of the collection of all compact convex sets of $\mathbb{R}^{n}$a Banach space

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edited Jan 7, 2017 at 14:58

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

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

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

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asked Jan 7, 2017 at 14:17

The anti-symmetric property of the collection of all compact convex sets of $\mathbb{R}^{n}$

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

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

gn.general-topology