Zero-dimensional closed set aposyndesis and hyperspaces

A continuum is a compact, Connected metric space. It is said that a continuum X is zero-dimensional closed set aposyndetic provided that for each zero-dimensional closed subset A of X and for each p is an element of X - A, there exists a subcontinuum M of X such that p is an element of IntM and M boolean AND A = 0. It is shown that if X is a continuum and n is an element of N, then both 2(X), the hyperspace of nonempty closed subsets of X, and C-n(X), the n-fold hyperspace of X, are zero-dimensional closed set aposyndetic.