On Lipschitz Ball Noncollapsing Functions and Uniform Co-lipschitz Mappings of the Plane
نویسنده
چکیده
is called the modulus of (uniform) continuity of f . The mapping f is said to be uniformly continuous if Ω f (d) → 0 as d ↓ 0. In this case the modulus of continuity is a subadditive monotone continuous function. The definition of Ω f implies that f (Br(x)) ⊂ BΩ f (r)( f (x)). (By Bρ(y) and Bρ(y) we denote, respectively, the open and the closed ball of radius ρ, centered at y.) One important class of uniformly continuous mappings is the class of Lipschitz mappings, that is, those satisfying Ω f (d) ≤ Ld for some positive L. The least such L is called the Lipschitz constant of the mapping f . In a similar way, couniformly continuous mappings are defined as those satisfying
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