The topology of continua that are approximated by disjoint subcontinua

Suppose that is a collection of disjoint subcontinua of continuum X such that limi→∞dH(Yi,X)=0 where dH is the Hausdorff metric. Then the following are true:(1)X is non-Suslinean.(2)If each Yi is chainable and X is finitely cyclic, then X is indecomposable or the union of 2 indecomposable subcontinua.(3)If X is G-like, then X is indecomposable.(4)If all lie in the same ray and X is finitely cyclic, then X is indecomposable.