$(X,\mathcal T)$ and $(Y,\mathcal S)$ are topological spaces. $X$ can be embedded homeomorphically in $Y$ and $Y$ can be imbedded homeomorphically in $X$.
Are $X$ and $Y$ homeomorphic?
How about uniform spaces?
2026-02-24 00:31:19.1771893079
Anti-symmetric property of embedding in topological spaces.
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Not in general. The Cantor set minus any one point and the Cantor set itself are a counterexample, as are $[0,1]$ and $(0,1)$ and many others.