Abstract
SynopsisLet I be the group of rotations of the circle and suppose that a map f from I into I is “almost linear”. More precisely, let ε be a positive real number and suppose that d(f(x)+f(y), f(x + y))<ε for all x and y in I; f is said to be an ε-homomorphism. If ε is sufficiently small, then a homomorphism h from I into I can be constructed such that d(f(x), h(x))≦ε for all x in I. This result is refined and generalized in several ways.
Publisher
Cambridge University Press (CUP)
Cited by
14 articles.
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