LOCAL SET APPROXIMATION: MATTILA–VUORINEN TYPE SETS, REIFENBERG TYPE SETS, AND TANGENT SETS
نویسندگان
چکیده
منابع مشابه
Local Set Approximation: Mattila–vuorinen Type Sets, Reifenberg Type Sets, and Tangent Sets
We investigate the interplay between the local and asymptotic geometry of a set A ⊆ Rn and the geometry of model sets S ⊂ P(Rn), which approximate A locally uniformly on small scales. The framework for local set approximation developed in this paper unifies and extends ideas of Jones, Mattila and Vuorinen, Reifenberg, and Preiss. We indicate several applications of this framework to variational...
متن کاملLocal Approximation of Semialgebraic Sets and Tangent Cones
Tangent cones Let A ⊆ R be a closed semialgebraic (s.a.) set and assume from now on that the origin O is not an isolated point of A. We recall that the tangent cone to A at O is the set C(A) = {u ∈ R|u = lim k→∞ tkxk}, where {xk} ⊂ A tends to O and {tk} ⊂ R. If we allow tk ∈ R only, we get what we call the tangent semicone to A at O, which we denote with C(A). It is easy to show that both C(A) ...
متن کاملInterval Type-2 Fuzzy Rough Sets and Interval Type-2 Fuzzy Closure Spaces
The purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.
متن کاملReifenberg Parameterizations for Sets with Holes
We extend the proof of Reifenberg’s Topological Disk Theorem to allow the case of sets with holes, and give sufficient conditions on a set E for the existence of a bi-Lipschitz parameterization of E by a d-dimensional plane or smooth manifold. Such a condition is expressed in terms of square summability for the P. Jones numbers β1(x, r). In particular, it applies in the locally Ahlfors-regular ...
متن کاملEquilibrium Cantor-type Sets
Equilibrium Cantor-type sets are suggested. This allows to obtain Green functions with various moduli of continuity and compact sets with preassigned growth of Markov’s factors.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Forum of Mathematics, Sigma
سال: 2015
ISSN: 2050-5094
DOI: 10.1017/fms.2015.26