On Finitely Equivalent Continua

A continuum means a compact connected metric space. For a positive integer n, a continuum X is said to be n-equivalent provided that X contains exactlyn topologically distinct subcontinua. A continuumX is said to be hereditarily n-equivalent provided that each nondegenerate subcontinuum of X is n-equivalent. If there exists a positive integer n such that X is n-equivalent, then X is said to be finitely equivalent. Thus, for n = 1, the concepts of “1equivalent” and “hereditarily 1-equivalent” coincide, and they mean the same as “hereditarily equivalent” in the sense considered, for example, by Cook in [2]. Observe the following statement.