拟共形映照和线性局部连通集

Quasiconformal Mappings and Linearly Locally Connected Sets

本文证明了Ｒｎ中线性局部连通集定义中的两个性质分别在保持无穷远点不变的拟共形映照下是不变的，并且指出保持无穷远点不变的条件是必不可少的．反过来，设ｆ是Ｒｎ上的同胚，ｆ（ ）＝ ，若线性局部连通集定义中的任意一条性质在ｆ下不变，则ｆ必是拟共形映照．

In this paper, we proved that the two conditions of linearly locally connectivity are invariant respectively under quasiconformal mappings which fixed the infinity and pointed out the condition-of fixed the infinity is essential by giving an example. On the other hand, we proved the converse of above results are true also.