A unital subalgebra A ⊆ C(X) (X compact Hausdorff) that separates points is dense in C(X) w.r.t. the uniform norm. Weierstrass polynomial approximation is the classical special case.
Stone–Weierstrass theorem
Related concepts
- Continuity
- Compactness
- Hausdorff (T₂) space
- Bernstein polynomials B_{k,n}(x): partition of unity + Weierstrass proof
- Bernstein partition-of-unity n=2: Σ_k B_{k,2}(x) ≡ 1; midpoint (1/4,1/2,1/4)
- Weierstrass approximation (1885)
- Muntz-Szasz theorem (1914)
- Milankovitch orbital forcing: F(t) = sum A_k cos(omega_k t); spectrum on 3 frequencies
- Machine-learning potentials (NNP, GAP)