The Topology Of Continua That Are Approximated By Disjoint Subcontinua

摘要

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) X is non-Suslinean. (2) If each Y_i 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 {Y_i}_(i=1)~∞ all lie in the same ray and X is finitely cyclic, then X is indecomposable.