An extendability condition for bilipschitz functions |
| |
Authors: | D A Trotsenko |
| |
Institution: | 1.Sobolev Institute of Mathematics Novosibirsk State University,Novosibirsk,Russia |
| |
Abstract: | We give a new definition of λ-relatively connected set, some generalization of a uniformly perfect set. This definition is equivalent to the old definition for large λ but makes it possible to obtain stable properties for small λ. We prove the λ-relative connectedness of Cantor sets for corresponding λ. The main result is as follows: A ? ? admits the extension of all M-bilipschitz functions f: A → ? to M-bilipschitz functions F: ? → ? if and only if A is λ-relatively connected. We give exact estimates of the dependence of M and λ. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|