连续型2^∞单峰映射的逆向限空间

On Inverse Limit Space of Continuous Type 2∞ Unimodal Mapping

设Ｉ是一个闭区间［０，１］，且ｆ：Ｉ→Ｉ是一个连续型２∞单峰映射．本文作者研究了逆向限空间ｌｉｍ｛Ｉ，ｆ｝的结构，证明了：（１）Ｏｒｄｅｒ（ｌｉｍ｛Ｉ，ｆ｝）＝ｗ０当且仅当Ｍ同胚于康托集；（２）Ｏｒｄｅｒｌｉｍ｛Ｉ，ｆ｝＝ｗ０＋１当且仅当Ｍ不同胚于康托集．

Let I be a closed interval and f:I→I be a continuous type 2∞ unimodal mapping.We investigate the structure of the inverse limit space lim{I,f} and prove the following properties:(1) such as Order(lim{I,f})=w0 iff M is homeomorphic to the Cantor set,(2) such as Order(lim{I,f})=w0+1 iff M is not homeomorphic to the Cantor set.