The topology of continua that are approximated by disjoint subcontinua

Suppose that { Y i } i = 1 ∞ is a collection of disjoint subcontinua of continuum X such that lim i → ∞ d H ( Y i , X ) = 0 where d H is the Hausdorff metric. Then the following are true:(1) on-Suslinean. h Y i is chainable and X is finitely cyclic, then X is indecomposable or the union of 2 indecomposable subcontinua. s G-like, then X is indecomposable. i } i = 1 ∞ all lie in the same ray and X is finitely cyclic, then X is indecomposable.