What do we intuitively mean by embedding a manifold in an $n$-dimensional space?
Also, why does a circle look so differently when is is embedded in $3$-space than $2$-space?
2026-04-08 12:39:38.1775651978
What do we intuitively mean by embedding a manifold in an $n$-dimensional space?
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Intuitively, when we say "embed $M$ in $\Bbb R^n$", we mean "Find a subset of $\Bbb R^n$ which, with the inherited topology / differential structure, is homeomorphic / diffeomorphic to $M$."