Every smooth compact submanifold of R^n is isotopically approximable by real loci of nonsingular real algebraic subsets of C^n, settling a version of Nash's conjecture with uniformity for codim >=2.
Rudin.Real and Complex Analysis
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Optimal embedding dimension in the Nash--Tognoli theorem
Every smooth compact submanifold of R^n is isotopically approximable by real loci of nonsingular real algebraic subsets of C^n, settling a version of Nash's conjecture with uniformity for codim >=2.