Approaching solenoids and Knaster continua by rays

We prove that if Y   is a continuum containing a solenoid Σ such that R=Y∖ΣR=Y∖Σ is homeomorphic to [0,∞)[0,∞), then, there exists a retraction r of Y   to Σ. Moreover, any two such retractions are homotopic. It follows that if PRPR is the arc component of Σ containing r(R)r(R), then PRPR 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∖KR=Y∖K is homeomorphic to [0,∞)[0,∞) and cl(R)=Y. Let e denote the endpoint of R   and let x∈Kx∈K. Then there exists a retraction r of Y to K   such that r(e)=xr(e)=x.