科研之友
微信
新浪微博
Facebook
分享链接
摘要
We prove that if Y is a continuum containing a solenoid Sigma such that R = Y \ Sigma is homeomorphic to [0, infinity), then, there exists a retraction r of Y to Sigma. Moreover, any two such retractions are homotopic. It follows that if P-R is the arc component of Sigma containing r (R), then P-R is invariant under every homeomorphism of Y into itself. We also prove the following theorem for Knaster continua. Suppose Y is a continuum containing a Knaster continuum K such that R = Y \ K is homeomorphic to [0, infinity) and cl (R) = Y. Let e denote the endpoint of R and let x is an element of K. Then there exists a retraction r of Y to K such that r (e) = x.
- 出版日期2015-9-15
