Let $k$ be an algebraically closed field. For each $n \in \mathbb N$, we can equip the affine space $\mathbb A^n(k)$ with Zariski topology. For which $m,n$, are the affine spaces $\mathbb A^n(k)$ and $\mathbb A^m(k)$ , with Zariski topology, are homeomorphic ?
2026-03-25 01:18:51.1774401531
For which $m,n$, are the affine spaces $\mathbb A^n(k)$ and $\mathbb A^m(k)$ , with Zariski topology, are homeomorphic?
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The maximal length of a chain of closed irreducible subsets is a topological invariant. Therefore, if and only if $n=m$.