KnowraWeierstrass approximation theoremLinked fromLinked fromThe 10 pages that link to Weierstrass approximation theorem, each with the reason it gives.All 10Broader topic 1Related 6Compared with 3ContinuityRelated: Continuity is precisely the condition that permits uniform polynomial approximation on such intervals.Pointwise convergenceRelated: Its stronger uniform conclusion guarantees pointwise convergence of polynomial approximations.Supremum normRelated: Its approximation error is naturally measured by the supremum norm.Rational approximationRelated: It establishes polynomial approximation’s broad guarantee, independent of rational methods.Bounded functionRelated: Continuous functions on compact intervals are bounded, making uniform approximation meaningful.Runge's theoremCompared with: It is a real-variable predecessor to approximation results for holomorphic functions.Stone–Weierstrass theoremBroader topic: It is the interval case that the Stone–Weierstrass theorem substantially generalizes.Weierstrass M-testCompared with: Despite the shared name and uniform convergence, this is an approximation theorem, not a series test.Fejér's theoremRelated: Fejér means give a trigonometric route to uniform approximation for continuous periodic functions.Mergelyan's theoremCompared with: Unlike Mergelyan’s theorem, it needs no holomorphicity because its domain is a real interval.